A speeding car traveling north at 80mph passes the tramway intersection when the police begin pursuit. The police start 6 miles south of tramway traveling at 100mph. How many miles north of tramway will they be when they catch up with the speeding car?

Refer to the diagram shown below.

Define

x = distance, miles, that the speeding car travels before the police catch up.

t = time, hrs, before the police catch up.

Then

(80 m/h) * (t h) = (x mi)

80t = x (1)

(100 mi/h) * (t h) = (x+6 mi)

100t = x + 6 (2)

Subtract (1) from (2).

100t - 80t = x+6 - x

20t = 6

t = 6/20 = 0.3 h

From (1), obtain

x = 80*0.3 = 24 mi.

Answer: 24 miles