Question

A 4-mile stretch of highway on one place averages about 55,000 cars during rush hour. The average driver has an accident every 165,000 miles. Now, suppose I drive the route to work during rush hour and each accident in that portion of the highway slows me down by 10 min. There is a rule at work: $5 if you are at work at time, pay $10 if you're 10 minutes late, and pay $40 if you're 20min late or more. If I leave so that I can plan to arrive at work 15min early, how much money should I expect to receive or pay each day.

Answer 1

Given that an average driver has an accident every 165,000 miles.

Therefore on an average, there are accidents every mile for a single driver There are accidents in the 4-mile stretch for a single driver.

Given that, on an average, there are 55,000 cars during rush hour on the 4-mile stretch.

Therefore the total number of accidents in the 4-mile stretch on an average =

Given that each accident in the 4-mile stretch slows you by 10 minutes.

Therefore 1.33 accidents slow you by 1.33*10 = 13.3 minutes.

But you have left to work so that you can arrive 15 minutes early. So on an average, you reach on time most of the days.

Therefore you can expect to receive $5 each day.