Mathematics College

Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 5 mi/h. How long (in hours) will it be before Amanda catches up to Ben?

Answers

Answer 1

Answer:

2 hours 15 minutes

Step-by-step explanation:

Given that :

Ben's speed = 3 mi/hr

One and half hours after Ben leaves = 1.5 hours

Ben's distance = 3 mi/hr * 1.5 = 4.5 miles

Amanda's speed = 5 mi/hr

Time taken before Amanda catches up:

Let time taken = x

Distance = speed * time

Ben's distance = Amanda's distance

4.5 mi + (3 * x) = 5 * x

4.5 + 3x = 5x

4.5 = 5x - 3x

4.5 = 2x

x = 4.5 / 2

x = 2.25 hours

Time taken = 2.25 * 60 = 135 minutes = 2 hours 15 minutes

Answer 2

It would take Amanda 2.25 hours to catch up with Ben

Speed is the ratio of distance to time. It is given by:

Speed = distance/time

Given that Ben covers a distance d at time t, hence:

3 = d/t

d = 3t

Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5

5 = d/(t - 1.5)

d = 5t - 7.5

Since they catch up, hence:

3t = 5t - 7.5

2t = 7.5

t = 3.75 hours

Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours

Hence it would take Amanda 2.25 hours to catch up with Ben.

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Related Questions

The length of a rectangle is 2x + 3. The width of the rectangle is x - 2. Which of the following represents the perimeter of the rectangle?

Answers

Answer:

6x+2

Step-by-step explanation:

The perimeter is the sum of all of the sides. A rectangle has four sides. You multiply each equation by two, and add the two equations together.

To get the perimeter, you have to add all sides. So you’ll have 2x+3+2x+3+x-2+x-2. So assuming I have done the math correctly, the answer should be 6x+2.
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