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You are here: Experts > Science > Math for Kids > Word Problems > Uniform Motion Problem
Expert: Scott A Wilson - 10/30/2009
Question
A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 h.
Answer
Time for P is time for F + 2. Both meet after 3 hours. Speed of F is speed of P - 20.
This says that the time for P was 3, so the time for F was P+2=5.
Take the speed of F as F. This says that the speed of P is F+20.
The equation is then 3(F+20) = 5F.
That says that 3F+60=5F, so 2F=60, so F=30.
This says the P=50.
Verify
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To test these, we has travelled 3 hours at 50 mph, for 150 miles.
Train F has travelled 5 hours at 30 mph for 150 miles.
It looks like they met at 150 miles.
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