Question

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels

12
miles per hour slower than the westbound train. If the two trains are
850
miles apart after
5
hours, what is the rate of the eastbound train?

Answer 1

80 miles per hour

Explanation:

Eastbound

r = r - 12

t = 5 hours

d = d_e

Westbound

r = r

t = 5 hours

d_w = 850 - d

The two distances add up to 850 miles

d_w + d_e = 850 miles

(r * t)_w + ( (r -12)*5 ) = 850 miles

r*5 + (r - 12) * 5 = 850 Pull out 5 as a common factor

5 * ( r + r - 12) = 850 Divide by 5

(r + r - 12) * 5/5 = 850/5 Do the cancellation

2r - 12 = 170 Add 12 to both sides

2r - 12 + 12 = 172 + 12

2r = 184 Divide by 2

r = 92

r = the westbound train = 92 mph

r - 12 = The eastbound train = 80 mph