SOLUTION: I am really struggling with this. Could you please show me step by step how to solve this? The speed of train A is 20mph slower than the speed of train B. Train A travels 190 mile

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Question 456557: I am really struggling with this. Could you please show me step by step how to solve this?
The speed of train A is 20mph slower than the speed of train B. Train A travels 190 miles in the same time it takes train B to travel 290 miles. Find the speed of each train.
Thanks!! Was never good at word problems.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = speed of train A
Let b = speed of train B
:
Write an equation for each statement:
:
"the speed of train A is 20mph slower than the speed of train B."
a = b - 20
:
" Train A travels 190 miles in the same time it takes train B to travel 290 miles.
Write a time equation; time = dist/speed
a's time = b's time
190%2Fa = 290%2Fb
From the 1st equation, replace a with (b-20), and you have:
190%2F%28%28b-20%29%29 = 290%2Fb
Cross multiply
290(b-20) = 190b
290b - 5800 = 190b
290b - 190b = 5800
100b = 5800
b = 5800%2F100
b = 58 mph is train B
then
58 - 20 = 38 mph is Train A
;
:
We can confirm this solution by finding the time of each train (should be the same)
190/38 = 5 hrs
290/58 = 5 hrs
:
Did this make sense to you?
Find the speed of each train.