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

Answer:

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

Step-by-step explanation:

A. Car rate

          Let c = the car rate

Then c - 40 = bus rate

   Distance = rate × time

         Time = distance/rate

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

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

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:

$\begin{array}{rcl}\dfrac{540}{60} & = & \dfrac{180}{20}\\\\9 & = & 9\\\end{array}$

OK.