2 runners start the race at the same time. The first runners speed was 4/5 of the speed of the second runner. After 30 minutes, the runners are 2 miles apart. What is the speed of each runner?
Let the speed of the second runner be x mph.
Then the speed of the first runner is 4/5 * x = (4/5)x mph.
In 30 minutes, the first runner will have traveled 30*(4/5)x = (24/5)x miles.
And the second runner will have traveled 30*x = 30x miles.
Since they are 2 miles apart, we can set up an equation:
30x - (24/5)x = 2
Solving for x:
(150/5)x - (24/5)x = 2
(126/5)x = 2
x = 2 * 5 / 126
x = 10 / 63
So, the speed of the second runner is 10/63 mph.
And the speed of the first runner is (4/5)*(10/63) = 8/63 mph.