Two trains leave the station at the same time, one heading west and the other east. the westbound train travels 20 miles per hour faster than the eastbound train. if the two trains are 800 miles apart after 5 hours, what is the rate of the westbound train?

Givens

W = E + 20

d = 800 miles

d1 = Westbound train.

d2 = Eastbound train.

t = 5 hours.

Equations

West bound

W*5 = d1 miles

d1 = W*5

East bound

E*5 = (800 - d1)

Step One

Substitute d1 into the Eastbound train.

E*5 = (800 - 5*W)

Step Two

Substitute E = W + 20 on the left side of the above equation.

(W + 20)5 = 800 - 5W

Step Three

Solve Remove the brackets

5W + 100 = 800 - 5W Add 5W to both sides.

10W + 100 = 800 Subtract 100 from both sides.

10W = 800 - 100

10W = 700

W = 700/10

W = 70

E = W + 20

E = 70 + 10 = 90

Check

70*5 = 350

90*5 = 450

Total distance = 800

the answer is 5636.7