Question

A truck can travel 245 miles in the same time that it takes a car to travel 315 miles. If thetruck's rate is 10 miles per hour slower than the car's, find the average rate for each.

Answer 1

Let speed of car = v

speed of truck = v - 10

distance = speed x time

for car

315 = v x t

315 = vt

t = 315/v ------------------ 1

for truck

245 = (v - 10) x t ----------- 2

Next substitute equation 1 from car tp equation 2 in the truck.

$\begin{gathered} 245\text{ = (v - 10) x }\frac{315}{v} \\ \text{cross multiply} \\ 245v\text{ = 315 (v - 10) } \\ \text{divide through by 35} \\ 7v\text{ = 9(v - 10)} \end{gathered}$

$\begin{gathered} \\ 7v\text{ = 9v - 90} \\ 90\text{ = 9v - 7v} \\ 90\text{ = 2v} \\ v\text{ = 45} \end{gathered}$

The average speed of car = 45 miles per hour

The average speed of truck = 45 - 10 = 35 miles per hour