A runner starts at the beginning of a runners path and runs

A runner starts at the beginning of a runners\' path and runs at a constant rate of 3 mi/hr. Eight minutes later a second runner begins at the same point, running at a rate of 5 mi/hr and following the same course. How long will it take the second runner to reach the first?

Solution

Lets say second runner cathes first one after x hrs

So, distance travelled by 2nd runner = 5*x miles

Ist runner ran for x+ 8/60 hrs

So, distanec travelled by 1 st runner = 3*(x +8/60)

Now 5*x =3*(x +8/60)

5x = 3x + 8/20

2x = 8/20

x = 4/50 hrs

x = 4*60/50 = 24/5 = 4.8 minutes

second runner to reach the first after 4.8 minutes