Please help algebra word problem

Question

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 75 miles per hour. The eastbound train travels at 95 miles per hour. How long will it take for the two trains to be 272 miles apart?

Answer 1

distance (d) = rate (v) * time (t)

 

Since the two trains are heading in opposite directions then the distances of each are additive

D = d1 + d2

 

rate1 = 75 mph (train1)

rate2 = 95 mph (train2)

 

Since they both leave the same point at t = 0,

 

D = d1 + d2 = rate1*t + rate2*t  = t*(rate1 + rate2)

 

D = t*(rate1 + rate2) = 272 miles    and solve for t

 

t = D/(rate1 + rate2) = 272 miles/(75+95)mph = (272/170)hr = 1.6 hr (or 1 hr 36 min)