Question

Train A has a speed 30 miles per hour greater than that of train B. If train A travels 300 miles in the same times train B travels 180 miles what are the speeds of the two trains?

Answer 1

Step 1: Write out the formula

$\text{ time = }\frac{\text{ distance}}{\text{ spe}ed}$

Step 2: Find the time taken by A to travel 300miles.

$\begin{gathered} \text{Let the sp}eed\text{ of train B be }x\text{.} \\ Therefore, \\ \text{speed of train A = }x+30 \end{gathered}$

in this case,

$\text{distance = 300 miles}$

Therefore,

$\text{time = }\frac{300}{x+30}$

Step 3: Find the time taken by B to travel 180miles

$\begin{gathered} \text{ In this case} \\ \text{ distance = 180 miles} \\ \text{ sp}eed\text{ = x miles per hour} \end{gathered}$

Then

$\text{time = }\frac{\text{ 18}0}{\text{x}}$

Step 4: Find x

Since the time A travels 300 miles is the same time B travels 180 miles, then

$\begin{gathered} \frac{300}{x+30}=\frac{180}{x} \\ \text{Dividing both sides by 30 we have} \\ \frac{10}{x+30}=\frac{6}{x} \\ \text{Cross}-\text{ multiplying, we have} \\ 10x=6(x+30) \\ \end{gathered}$

Expanding, we have

$\begin{gathered} 10x=6x+180 \\ 10x-6x=180 \\ 4x=180 \\ \text{ Dividing both sides by 4, we have} \\ x=\frac{180}{4}=45 \\ \text{speed of train A = 45 + 30 = 75 miles per hour} \end{gathered}$

Therefore, the speed of train B is 45 miles per hour and that of train A is 75 miles per hour