Josh and Karen live 20 miles apart and at exactly 2 pm, both decide to ride their bikes towards each other's houses so that they can meet on the path somewhere in between. Josh rides at an average speed of 15 miles per hour and Karen rides at an average speed of 10 miles per hour. If Josh takes a 10 minute break after he starts to look at some birds while Karen rides the whole time, how many miles from Karen's house will they meet?

Answers

Answer 1

Answer:

They will meet at a distance 9 miles from Karen's house.

Step-by-step explanation:

Let the distance covered by Josh be [tex]S_{1}[/tex] and the distance covered by Karen be [tex]S_{2}[/tex]

The distance between Josh and Karen's houses is 20 miles. That is, the total distance both of them will cover is 20 miles.

Hence, [tex]S_{1} + S_{2} = 20 miles[/tex]

From the question, if Josh takes a 10 minute break after he starts while Karen rides the whole time, this means

If Karen rides for a total of [tex]t[/tex] mins, then Josh would spend [tex]t-10[/tex] mins for the journey

Also, Josh rides at an average speed of 15 miles per hour

and Karen rides at an average speed of 10 miles per hour

Now, for Josh

Distance = [tex]S_{1}[/tex]

Speed = 15 mile/hour (Covert to mile/minute); (NOTE: 1 hour = 60 mins)

Speed= 0.25 mile/min

Time spent = [tex]t - 10[/tex] mins

From

[tex]Speed =\frac{Distance}{Time}[/tex]

Distance = Speed × Time

Distance = 0.25 mile/min × (t-10) min

[tex]S_{1}[/tex] = 0.25(t-10) mile

[tex]S_{1}[/tex] = 0.25t - 2.5

t = ([tex]S_{1}[/tex] + 2.5) / 0.25 ....... (1)

For Karen,

Distance = [tex]S_{2}[/tex]

Speed = 10 mile/hour (Covert to mile/minute);

Speed= [tex]\frac{1}{6}[/tex] mile/min

Time spent = t

[tex]Speed =\frac{Distance}{Time}[/tex]

Distance = Speed × Time

Then, [tex]S_{2}[/tex] = [tex]\frac{1}{6}[/tex] mile/min × t min

[tex]S_{2}[/tex] = [tex]\frac{1}{6}t[/tex] mile

t = 6[tex]S_{2}[/tex] ......... (2)

Equating equations (1) and (2), we get

([tex]S_{1}[/tex] + 2.5) / 0.25 = 6[tex]S_{2}[/tex]

Then,

([tex]S_{1}[/tex] + 2.5) = 1.5[tex]S_{2}[/tex]

Recall that

[tex]S_{1} + S_{2} = 20 miles[/tex]

Then, [tex]S_{1} = 20 - S_{2}[/tex]

∴[tex]20 - S_{2}[/tex] + 2.5 = 1.5[tex]S_{2}[/tex]

2.5[tex]S_{2}[/tex] = 22.5

[tex]S_{2}[/tex] = 22.5 / 2.5

[tex]S_{2}[/tex] = 9 miles

This means Karen covers a total distance of 9 miles

Hence, they will meet at a distance 9 miles from Karen's house.


Related Questions

which value is a solution to the inequality 2x-5<-12?

Answers

Answer:

x < -4

Step-by-step explanation:

2x-5<-12, add 5 to both sides so then you get 2x<-8, then divide by two, x<-4 and your answer!

Answer: x<7/2

Step-by-step explanation:

Step 1. You are moving the constant, 5, to the right-hand side and changing the sign from a - to a +. Your new inequality is 2x<-12+5.

Step 2. Calculate the sum. You are adding -12 and 5. This is what your new inequality looks like: 2x<-7.

Step 3 (final step). You will now divide both sides by 2, and you will get a final answer of x<-7/2.

Hope this helps!

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Answers

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Answer:

1.5 in a decimal

Step-by-step explanation:

i hope it helps

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Answers

Answer:

n = 14

Step-by-step explanation:

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n = 14

Answer:

n=14

Step-by-step explanation:

n+4/-2 = -9

n+4 = 18

Hope it helps :3

Somebody please help me make some sense out of this:

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Answers

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Answers

Answer:

g = S - c

Step-by-step explanation:

Isolate the variable, g. Note the equal sign, what you do to one side, you do to the other. Simply subtract c from both sides:

S = g + c

S (-c) = g + c (-c)

S - c = g

g = S - c is your answer.

~

(URGENT) Country A produces about four times the amount of diamonds in carats produced in country B. If the total produced in both countries is 20,000,000 carats, find the amount produced in each country.

Answers

Answer:

A: 16,000,000 caratsB: 4,000,000 carats

Step-by-step explanation:

If the ratio is ...

  A : B = 4 : 1

Then the ratio to the total is ...

  A : total = 4 : (4+1) = 4 : 5

  B : total = 1 : (4+1) = 1 : 5

Country A produces (4/5)×20 M carats, or 16 million carats.

Country B produces the remainder, 4 million carats.

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Answers

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Wade Ellis buys a new car for $16,183.11. He puts 10% down and obtains a simple interest amortized loan for the rest at 11 1/2% interest for four years. How do we find his monthly payment and total interest

Answers

Answer:

If a new car was purchased for a cost of $16,183.11, and a down payment of 10% of the value was made, the initial payment was $1,618.31.

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6th grade math please help thx!!​

Answers

The answer is 26 so that means the quotient is 26.

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Answers

Answer:

30x-18

Step-by-step explanation:

(6)(5x+−3)

=(6)(5x)+(6)(−3)

=30x-18

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Answers

Answer:

  -1 -3i

Step-by-step explanation:

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−20

1.6

−1

0

Answers

Answer:

-8

Step-by-step explanation:

substitute X with -2 across the equation

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+2 - 10

= -8

Help pls I will mark you brainliest

Answers

Answer:

no#2

Step-by-step explanation:

In the figure shown, suppose m angle ABC=n and m angle ABD=2(m angle DBC). The angle bisector of angle DBC is BE. What is m angle EBC

Answers

Answer:

n/6

Step-by-step explanation:

If angle bisector of angle DBC is BE. What is m angle EBC, then <DBE = <EBC

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n = 2<DBC+<DBC

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<DBC = n/3

Since <DBC = 2EBC

n/3 = 2<EBC

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SIMPLIFY THE EXPRESSION THEN MATCH TO ANSWER (USE ORDER OF OPERATIONS) PLS HELP I DONT UNDERSTAND TY I APPRECIATE IT

Answers

plz I need a link to solve that

Rewrite the quality 827,000,000,000,000 pico second to show :

1sig. Fig.

2sig. Fig.

3sig. Fig.

4 dig. Fig.

5sig. Fig.

Answers

Answer:

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b. 2 sig. figs. 830,000,000,000,000 picoseconds (8.3 x 10^14 picoseconds)  

c. 3 sig. figs. 827,000,000,000,000 picoseconds (8.27 x 10^14 picoseconds)

d. 4 sig. figs. 827,000,000,000,000 picoseconds  (8.270 x 10^14 picoseconds)

e. 5 sig. figs. 827,000,000,000,000 picoseconds  (8.2700 x 10^14 picoseconds)

Step-by-step explanation:

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Answers

Answer:

Therefore the lenght of line segment is :√13

Step-by-step explanation:

Refer to the attachment for your answer.

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

rise over run

3/50

Answer:

A. 3/50

Step-by-step explanation:

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subtract the x values in the form where the first point is subracted from the second point: 3500-1000= 2500

then put these numbers in fraction form: 150/2500

simplify: 3/50

A jet plane can travel 567 miles per hour. How many mile can it travel in 4hour During the first trip and 6 Hour during the scon trip

Answers

It will take 8 hours to drive 120 miles at a speed of 15 miles per hour. Hi Mia, If you drive 15 mi per hour, you will be covering 15 miles each other you travel. If you know the total distance traveled, then you can simply divide it by speed to get the time it takes to cover that distance. explanation:

) Make a scatter plot of mice survival rate (response) against aspartame concentration (explanatory) and add the regression line. Described the direction, form, and strength of the relationship. What percent of the variation in mice survival rate can be explained by variations in aspartame concentrations

Answers

Answer & Step-by-step explanation:

Regression studies the relationship between independent / explanatory  (causal) variable, dependent / response (effected) variable. Scatter plot is a diagrammatic representation of regression.

Aspartame Concentration, being a toxic substance, is likely to have negative regression relationship with mice survival rate. It implies that higher concentration leads to lower mice survival, & lower concentration leads to higher mice survival.

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Answers

Answer:

2/3

Step-by-step explanation:

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The selection will happen between four women and six men

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= 10 people

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a) 2 women

b) 1 man and 1 woman

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A. $635
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C. $659
D. $661
E. $664
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Answers

Answer:

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Step-by-step explanation:

I guess I was help full for u

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3. A company makes a profit of $60 per software program and $45 per video game. The company can produce at most 300 software programs and at most 200 video games per week. Total production cannot exceed 400 items per week. How many items of each kind should be produced per week in order to maximize the profit? Use linear programming to solve. Show all your work. Answer:

Answers

Answer:

Step-by-step explanation:

This problem is a maximization problem

the objective is to maximize profit

let software program be x

and video program be y

the objective function is

60x+45y>P-------1

constrains

300x+200y<400------2

we can further reduce the expressions

3x+2y<4-----2

ASAP FASTER THAN THAT ITS DUE IN LIKE 30 OR LESS MINuTES
Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A.

Select ALL of the measurement pairs that could be the dimensions of Rectangle B.

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Could or could not(thats the question for all of them)
B. 8 inches by 2 inches
could or could not
C. 10 inches by 4 inches
could or could not

D. 13.5 inches by 4.5 inches
could or could not
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could or could not

Answers

Answer:

a,d,e could

Step-by-step explanation:

a-is 1/2 of rec a so yes

b-no

c-no

d-could it 1.5 of rec a

e-could it 10 times rec a


Describe the error in the work shown below.
Find an expression equivalent to 18 + 30.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1,2,3,5, 6, 10, 15, 30
18 + 30 = 6(3 + 10)


Pls help fast

Answers

The answer is 18+30= 6(3+5) when you distribute the given one 18+30= 6(3+10) which was wrong, you get 18+60 so u need to replace the 10 with something that will equal 30 when multiplied; which is 5.

number 27 please.. i can not figure it out.

Answers

Answer: x=-12

Step-by-step explanation:

To solve for x, you want to use algebraic properties to isolate x.

[tex]\frac{x}{4}=2+\frac{x-3}{3}[/tex]                       [subtract both sides by [tex]\frac{x-3}{3}[/tex]]

[tex]\frac{x}{4}-\frac{x-3}{3}=2[/tex]                       [get common denominator]

[tex]\frac{3x}{12} -\frac{4x-12}{12} =2[/tex]                  [subtract]

[tex]\frac{-x+12}{12} =2[/tex]                          [multiply both sides by 12]

[tex]-x+12=24[/tex]                     [subtract both sides by 12]

[tex]-x=12[/tex]                            [divide both sides by -1]

[tex]x=-12[/tex]

Now, we know that x=-12.

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Answers

Answer:

B. 4.62 x 10^5 is scientific notation of 462000

can you please help me ​

Answers

Answer:

The answer is true!

Step-by-step explanation:

Since B is in the middle and they both are congruent.

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Answers

0.6, 2/3, 9/16 ........
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