Pamela A. Bolton

Problem 1-4.23 Assignment Due: September 29, 2009

Problem Statement

Bill leaves Seattle at 2 P.M. traveling east on Interstate 90 at 45 miles per hour. Two hours later, Jim follows the same route, traveling 75 miles per hour. Assuming they maintain a constant speed, how long will Jim travel before passing Bill?

Output

How long will Jim travel before passing Bill?

Input

· Bill leaves Seattle at 2 P.M. traveling east on Interstate 90 at 45 miles per hour.

· Jim leave two hours later, Jim follows the same route, traveling 75 miles per hour.

· Assuming they both maintain a constant speed.

Process

Notation:

Not needed

Additional Information:

Not needed

Diagram:

Hour	0	1	2	3	4	5
Time	2:00	3:00	4:00	4:00	6:00	7:00
Bill	0	45	90	135	180	225
Jim	0	0	0	75	150	225

Approach:

Using the fact that Bill covers 45 miles each hour traveled and Jim covers 75 miles each hour traveled, compute the distance covered by each at the end of each hour.

Find the time when each has traveled the same distance.

Then determine Jim’s travel time.

Solution

Hour Time Bill’s Distance (miles) Jim’s Distance (miles

0 2p 0 0

1 3p 45 0

2 4p 90 0

3 5p 135 75

4 6p 180 150

5 7p 225 225

The distance traveled is the same for both after Bill traveled for 5 hours and Jim has travel for 3 hours. Thus it will take Jim 3 hours of travel to pass Bill.

Check

During the 2 hours before Jim starts, Bill travel 90 miles.

Thus , when Jim starts he has a 90-mile gap to close before passing Bill.

The gap is closed at the rate of 30 miles per hour, the difference in the two speeds.

Since the 90-mile gap will be closed at the rate of 30 miles each hour, it will take 3 hours to close the entire gap.

It will take Jim 3 hours to pass Bill.

The solution checks.