Question

Two runners start from the same point at the same time. They will be 4 miles apart at the end of two hours if running in the same direction, and they will be 16 miles apart at the end of one hour if running in opposite directions. Find their speeds.

Answer 1

runner 1 runs with 9 miles / hour

runner 2 runs with 7 miles / hour

Explanation:

x = speed of runner 1

y = speed of runner 2

2 hours × (x miles / hour) - 2 hours × (y miles / hour) = 4 miles

2x - 2y = 4

x - y = 2

x = y + 2

1 hour × (x miles / hour) + 1 hour × (y miles / hour) = 16

x + y = 16

y + 2 + y = 16

2y + 2 = 16

2y = 14

y = 7 miles / hour

x = y + 2 = 9 miles / hour