Question

Train A has a speed 15 miles per hour greater than that of train B. If train A travels 310 miles in the same times train B travels 280 mileswhat are the speeds of the two trains?

Answer 1

From the question given, we can infere the following information:

If the speed of trian B = b (miles/ hour)

Then speed of train A = 15 + b (miles/ hour)

Also, we know that

$\text{time = }\frac{dis\tan ce}{speed}$

Then train A travels 310 miles and train B travels 280 miles in equal time

so that for train A

$\text{time}_A=\frac{310}{15\text{ + b}}$

Also, for train B

$\text{time}_B=\frac{280}{b}$

Since time of train A and B are equal, we can equate the equations of the time for the two trains

$\begin{gathered} \text{time }_A=time_B=>_{} \\ \\ \frac{310}{15\text{ + b}}\text{ =}\frac{280}{b} \end{gathered}$

The next step is to cross multiply the expression above, so that

310 x b = 280 (15 + b)

310b = 280 x 15 + 280 x b

310b = 4200 + 280b

Collecting like terms

310b - 280b = 4200

30b = 4200

Divide both sides by 30

b = 4200/30

b = 140

so the speed of the train B is 140 miles per hour

Train B = 140 miles/hour

From the relationship between A and B, we have established earlier

Speed of Train A = Speed of Train B + 15

So the speed of Train A = 140 + 15

Train A = 155 miles/hour

The speed of Train A = 155 miles per hour and that of Train B is 140 miles per hour