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 = }(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} (300)/(x+30)=(180)/(x) \\ \text{Dividing both sides by 30 we have} \\ (10)/(x+30)=(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=(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