# Mr. Williams starts out in his auto traveling 30 miles per hour. Four hours later, Mr. Speedster starts out at the same point at 60 miles per hour to overtake Mr. Williams. In how many hours will he be overtaken?

Since Mr. Williiams travels at 30 mph, in after time t (in hours) have elapsed, he will have traveled the distance d

d = 30t

Mr. Speedster starts out at the same point 4 hours later at 60 mph. So after time t have elapsed since Mr. Speedster started, he will have traveled for t - 4 hours and covered the distance 60(t-4).

At the time t when Mr. Speedster overtakes Mr. Williams, they will have traveled the same distance d:

d = 30t = 60(t - 4)

Solve this equation for t:

30 t = 60t - 240

-30t =-240

t = 8

8 hours have elapsed since Mr. Williams started traveling, so 8 - 4 = 4 hours have elapsed since Mr. Speedster started traveling.

Mr. Speedster will overtake Mr. Williams in 4 hours.

This means Mr. Speedster will overtake Mr. Williams in 8 hours after

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