Expert: Socrates - 9/30/2009

Question
Train A travels 12 mph slower than Train B. Train travels 200 miles in the same time it takes Train B to travel 260 miles. Find the speed of each train.
The first time I did this, I got Train A travelling 40mph, and Train B travelling 52mph. The second time Train A was 38 and Train B was 50. I don't know which is right, or if either is right.

Answer
Let b be the speed of train B , and let a be the speed of train A.
Train A travels 12 mph slower than Train B , so a = b - 12

It takes train B 260/b hours to travel 260 miles

It takes train A 200/a hours to travel 200 miles

We are told that these times are the same , so

260/b = 200/a

We also know that a = b - 12 , so

260/b = 200/(b - 12)

Cross multiply

(260)(b-12) = 200b


simplify

260b - 3,120 = 200b

60b = 3,120

6b = 312

b = 52

Train B travels at 52 mph

For train A , a = b - 12 = 52 - 12 = 40

Train A travels at 40 mph.


You can check these answers

260/52 = 5 hours

200/40 = 5 hours

the times are the same


The speeds are


a = 40 , b = 52