word problems in algebra

Question

A runner starts at the beginning of a runners' path and runs at a constant rate of 6 mi/hr. Fifteen minutes later a second runner begins at the same point, running at a rate of 8 mi/hr and following the same course. How long will it take the second runner to reach the first?

  min

Answer 1

15 minutes = 1/4 of an hour

First runner runs for t hours

Second runner runs for t-15 minutes

distance = rate of speed x time

d=rt

distance is the same for both runners

d=6t = 8(t-1/4)

6t = 8t - 2

8t-6t = 2

2t = 2

t = 1 hour

First runner runs for an hour

Second runner runs for 45 minutes when he or she catches up

45 minutes = 3/4 of an hour

8 x 3/4 = 6 miles

6 x 1 = 6 miles

each ran 6 miles, one hour after the first runner began.