Dillard Drive Problem of the Week

Week Five– September 22-26 ANSWER

TRUCKER PROBLEM

PROBLEM: After a good night’s sleep, Mr. Hostetter, truck driver for Roehl Transport, is awakened at 7:30a.m. on April 1st by a call from his dispatcher. His dispatcher has a load for him to take to Porter, IN, right away. Porter is 510 miles away. He plans as if the trip were 10% longer because of detours, traffic jams, etc. All of Roehl truck drivers average 50 miles per hour.

·  U.S. DOT regulations prohibit a driver from driving more than 70 hours in an 8-day period. Over the past 7 days, Mr. Hostetter has accumulated 54 and ¾ hours.

·  At 8pm, Mr. Hostetter’s log looks like the chart below. DOT regulations state that no driver shall drive more than 10 hours without following it with eight consecutive hours off duty.

Driver’s Daily Log April 1st

Midnight – 8am rest 8 hrs/no driving / Off duty
8am – 8:15am no driving / Truck inspection
8:15am – 1pm 4hr 45 min driving / Driving
1pm – 1:30pm ½ hour no driving / Off duty
1:30pm – 6:30pm 5 hours driving / Driving
6:30pm – 6:45pm 15 min no driving / Truck inspection
6:45pm – 8pm 1hr 15 min no driving / Off duty
8pm - / driving

Question 1: The trip is 510 miles. 10% of 510 is 51 miles. 510 + 51 = 561 total miles

561 ÷ 50 miles/hour = 11.22 hours for the drive or 11 hours and 12 or 13 minutes.

Does he have enough hours to deliver the freight?

·  How many has he logged so far? The story tells us 54 hours and 45 minutes

·  He is only allowed 70 hours in 8 days.

·  So, 70 hours – 54 hours/45 minutes = 15hours/15 minutes left.

·  YES, he has 11 hours and 13 minutes and that fits within the “window” of 15 hours/15 min.

What is the earliest Mr. Hostetter will arrive in Porter?

For this question we have to look carefully at the chart. He started driving at 8:15am and by 8pm he has driven 9hours and 45 minutes. The trip takes 11 hours and 13 minutes, so subtract:

·  11 hours 13min – 9 hours 45 min = 1hour and 28 minutes left to make the whole trip. (You can round that to 1 hour and ½.

·  Since he is required to rest after 10 hours, he can only drive another 15 minutes at 8pm before resting 8 hours.

·  8:15pm – rest 8 hours

·  Wake up time: 4:15am (I’m still asleep at that time!)

·  Remember the problem says there is a truck inspection for 15 minutes so now it is 4:30am

·  4:30am + 1 and ½ hours more to make the trip = 6am

ANSWER: THE EARLIEST HE WILL ARRIVE IN PORTER IS 6AM ON APRIL 2ND.