SOLUTION: train A leaves at 3, train B leaves at 8. train B is traveling 120mph faster than train A and passes train A at 10. what speeds are both trains traveling at?

Question 968186: train A leaves at 3, train B leaves at 8. train B is traveling 120mph faster than train A and passes train A at 10. what speeds are both trains traveling at?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
train A travels for 7 hours from 3 to 10 at x mph.
train B travels for 2 hours from 8 to 10 at x + 120 mph.
rate * time = distance.
when train B catches up to train A, they have both traveled the same distance.
formula for train A is 7x = d
formuls for train B is 2(x+120) = d
simplify to get:
7x = d
2x + 240 = d
subtract second equation from first equation to get:
5x - 240 = 0
add 240 to both sides of that equation to get 5x = 240
divide both sides of the equation by 5 to get x = 48
train A travels 7 hours at 48 mph for a total of 7 * 48 = 336 miles.
train B travels 2 hours at (48 + 120) = 160 mph for a total of 168 * 2 = 336 miles.
train B catches up to train A at the 336 mile mark.
train A is traveling at 48 mph and train B is traveling at 168 mph.

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