2 cars c and d started to move to each other car c was 118 miles from Boston car d was 256 miles from Boston car c was going twice as fast as car d how. Far from Boston will these 2 cars meet

Answer:

131.3 miles

Step-by-step explanation:

The two cars are moving from different directions. The total distance between the two cars = 118 miles + 256 miles = 374 miles.

Let us assume that the two cars meet at point O, let the distance between car c and O be d₁, the distance between car d and point O be d₂, hence:

d₁ + d₂ = 374 miles       (1)

Let speed of car d be x mph, therefore speed of car c = 2x mph (twice of car d). If it take the cars t hours to meet at the same point, hence

For car c:

2x = d₁/t

t = d₁ / 2x

For car d;

x = d₂/t

t = d₂/ x

Since it takes both cars the same time to meet at the same point, therefore:

d₁/2x = d₂ / x

d₁ = 2d₂

d₁ - 2d₂ = 0         (2)

Solving equation 1 and 2 simultaneously gives d₁ = 249.3 miles, d₂ = 124.7 miles

Therefore the distance from point of meet to Boston = 249.3 - 118 = 131.3 miles

   Both the cars will meet at 131.33 miles from Boston.

Given in the question,

Distance between two cars = 118 + 256 = 374 miles

Let these cars meet at a point P.

Let the distance between the car C and point P = 'x' miles

Therefore, distance between car D and point P = (374 - x) miles

Time taken 't' by car C to travel the distance 'x' miles,

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

[tex]t=\frac{x}{2v}[/tex]  -------(1)

Time taken 't' by the car D to travel (374 - x) miles,

[tex]t=\frac{(374-x)}{v}[/tex] ---------(2)

Substitute the value of 't' from equation (2) to equation (1),

[tex]\frac{x}{2v}=\frac{374-x}{v}[/tex]

[tex]\frac{x}{2}=374-x[/tex]

[tex]\frac{3x}{2}=374[/tex]

[tex]x=249.33\text{ miles}[/tex]

From the picture attached,

Distance between Boston and the meeting point = (x - 118) miles

                                                                                   = 249.33 - 118

                                                                                   = 131.33 miles

     Therefore, both the cars will meet at a point 131.33 miles distant from Boston.

Learn more about the system of equations here,

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