Expert: Josh - 7/10/2007

Question
A businessman drives from Washington, D.C. to Boston, a distance of 442 miles, and then makes the return trip.  On the way to Boston, he drives 65 miles per hour, taking a 1-hour rest stop during the drive.  After finishing his business in Boston, he makes the return trip driving at 60 miles per hour and takes a 45-minute rest stop halfway through the trip.

Which leg of the journey, Washington, D.C. to Boston, or Boston to Washington, D.C. takes the longer time


Answer
Hello Sean,

While the wheels are moving, the time (t) taken to cover a distance D at a speed of S is given by t=D/S.

From DC to Boston,
 D=442 [mile], S=65 [mile/hour],
 Thus, t1 = D/S = 442/65 = 6.8 [hour]
We add an extra one hour for the rest stop.
Total time = 7.8 [hour]

After finishing his business (lol), on the return leg, he still has to cover the same distance.
Time on road: t2 = 442/60 = 7.366666... [hour]
Adding 0.75 hour rest period, this gives 8.366666...hours.