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Question

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels
12
miles per hour slower than the eastbound train. If the two trains are
450
miles apart after
3
hours, what is the rate of the westbound train?

Answer 1

Rate * Time = Distance

 

We know the final time will be 3 hours and that the distance between the two trains is 450 miles after 3 hours.

Therefor the Rate * Time for each train will ADD together to give us 450 miles.  Remember the trains are going OPPOSITE directions from each other so the distance both cover adds together.  Also the rate will be in units of miles per hour.

 

Rate of west bound train = X-12

Rate of east bound train = X

 

(X-12) * 3 (hours) + X * 3 (hours)= 450 miles

 

3X-36 + 3X = 450

 

6X-36 = 450

 

6X = 486

 

6X/6 = 486/6

 

X = 81

 

Therefore the west bound train is going 69 miles per hour.  Plug 81 into X-12 and BAAAM!