Answer to January 13, 2003 Problem

by Michael Winckler

The Crew Problem

 
The Sherando bridge and the James Wood bridge are 1 mile apart. The Handley crew team starts rowing upstream at the James Wood bridge. As the crew passes under the Sherando bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously and has the crew go back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the James Wood bridge.

How fast is the river flowing?

 

Solution to the Problem:

Since the crew's speed is measured relative to the river and the hat is floating on the river, the time it takes the crew to get back to the hat is also 10 minutes. So, in 20 minutes the hat travelled 1 mile down the river. Therefore, the river's speed is 1 mile/20 minutes or 3 miles per hour.

Here is a second solution. I always solve these problems using a Rate-Time_Distance Table.
Let B = rate of the boat in still water.
Let R = rate of the river current.

  Rate (Mile/Min) Time (Minutes) Distance (Miles)
Hat (from Sherando to James Wood) R 1/R 1 mile
Boat (From Sherando upstream to turn-around point) B - R 10 minutes 10 (B - R)
Boat (from turn around point downstream to Sherando) B + R 10 (B - R)
Boat (From Sherando to James Wood) B + R 1 / (B + R) 1 mile


Correctly solved by:

1. Kathleen Altemose Winchester, Virginia
2. Rick Jones Kennett Square, Pennsylvania
3. Richard Johnson La Jolla, California
4. William Funk, Jr. San Antonio, Texas
5. John Funk Ventura, California
6. Jeffrey Gaither Winchester, Virginia
7. George Gaither Winchester, Virginia
8. Daniel Wilberger Winchester, Virginia