Determine the speed

Question

Two trains leave the same city at a right angle to each other and continue in straight lines. Train B travels 5 mph faster than train A. After two hours, they are 50 miles apart. Determine the speed of each train.

Answer 1

x is the speed of Train A

Train A travels 2x

Train B travels 2(x+5) = 2x+10

Pythagorean says: (2x)^2 + (2x+10)^2 = 2500

4x^2 + 4x^2 + 40x + 100 = 2500

8x^2 + 40x - 2400 = 0

x^2 + 5x - 300 = 0

( x + 20)(x - 15 ) = 0

x+20=0 results in negative measures

x-15=0 --> x = 15

The speeds are 15 and 20