Question

a car can travel 540 miles in the same time it takes a bus to travel 180 miles. if the rate of the bus is 40 miles per hour slower than the car, find the average rate for each.

Answer 1

`\large \boxed{\text{ Car = 60 mi/h: bus = 20 mi/h}}`

Explanation:

A. Car rate

Let c = the car rate

Then c - 40 = bus rate

Distance = rate × time

Time = distance/rate

`\begin{array}{rcll}(540)/(c) & = & (180)/(c - 40) & \\\\(540(c - 40))/(c) & = & 180 &\text{Multiplied each side by 180 - c}\\\\540(c - 40) & = & 180c & \text{Multiplied each side by c}\\540c - 21600 & = & 180c & \text{Distributed the 540}\\360c -21600 & = & 0 & \text{Subtracted 180c from each side}\\\end{array}\\`

`\begin{array}{rcll}360c & = &21600 &\text{Added 21600 to each side}\\c & = & (21600)/(360) & \text{Divided each side by 360}\\\\c & = & 60 &\text{Simplified}\\\end{array}\\\text{The average rate of the car is $\large \boxed{\textbf{60 mi/h}}$}`

B. Bus rate

`\text{Bus rate} = c - 40 =60 - 40 = \mathbf{20}\\\text{The average rate of the bus is $\large \boxed{\textbf{20 mi/h}}$}`

Check:

`\begin{array}{rcl}(540)/(60) & = & (180)/(20)\\\\9 & = & 9\\\end{array}`

OK.