What are the speeds of the cars?

Question

One car travels 490 miles in the same amount of time it takes a second car traveling 5 miles per hour slower than the first to go 455 miles. What are the speeds of the cars?

Answer 1

Hi Daniellia, the best way to solve a problem like this is with a table.

 

Let x be the rate, miles per hour of the first car. The x - 5 will be the rate, miles per hour of the second car.

 

In this problem, time will be the same for both cars.

 

To solve use the D(istance) = R(ate) * T(ime) equation.

 

Car     Distance        Rate       Time

----------------------------------------

1            490             x

 

2            455           x - 5

 

Car 1:

 

D = R * T

 

Substitute for D and R, solve for T:

 

490 = x * T

 

T = 490 / x

 

Car 2:

 

D = R * T

 

Substitute for D and R, solve for T:

 

T = 455 / (x - 5)

 

Since the time is the same for both cars, we can equate the two time equations:

 

490 / x = 455 / (x - 5)

 

Cross multiply:

 

490 * (x - 5) = 455 * x

 

Clear parenthesis:

 

490x - 2450 = 455x

 

Subtract 455x from both sides:

 

35x - 2450 = 0

 

Add 2450 to both sides:

 

35x = 2450

 

Divide both sides by 35:

 

x = 70

 

Car 1 traveled at 70 miles per hour.

 

Car 2 traveled at 70 - 5, or 65 miles per hour.

 

Questions?