A truck crosses the county line at 60 mph. Five minutes later, a sheriff crosses the border in hot pursuit, driving at 90 mph. How far from the border will the sheriff overtake the trucker?

Answer 1

5 minutes = 1/12 of an hour

d=rt, distance = rate of speed times time

d=60t = 90(t-1/12)

60t = 90t - 90/12

30t = 45/6

6t = 9/6 = 3/2

2t = 1/2

t = 1/4 hour = 15 minutes

in a quarter hour, the trucker went 1/4 of 60 miles = 15 miles

in 1/4 - 1/12 hour, the police went 1/6 of an hour at 90 = 90/6 = 15 miles