Question

Two trains are 500 miles apart when they first enter a collision course. If, after two hours, the distance between them is 300 miles and one train goes 20 mph faster than the other, find the speed of the faster train.

Answer 1

60 miles per hour. In two miles the sum of the distance the two trains traveled was 200 miles, you divide that by 2, the sum of the speed of the two trains is 100 miles per hour, now put the speed of the slow train as  x and the fast as x +20, the sum of x and x +20 is 100, so 2x + 20 =100, you subtract 20 from both sides, 2x = 80, divide by 2, x = 40, the problem asks for the speed of the fast train, so, x + 20 is 60.

Answer 2

60

Explanation:

slow train = x

fast train = x + 20

First we get the amount of distance both trains have covered

500 - 300 = 200

Next we have to divide it by the number of hours it took

200 ÷ 2 = 100

Then we write our equation

x + x + 20 = 100

2x + 20 = 100

Subtract 20 from both sides

2x = 80

Divide 2 from both sides and your left with

x = 40

Next we write our expression for the faster train

x + 20

Since we found that x is 40, we plug it into the expression which is

now an equation and we get...

40 + 20 = 60

Answer = 60 mph