1. Introduction to Distance-Rate-Time The following is designed to help you understand the basics of one of the popular application problems in introductory algebra: rate of a canoe on a river. Example 1: Sam can paddle his canoe on a lake at 4 miles per hour. What will his rate be when he rows his canoe: a) up a river, against a current of 2 mph? b) down a river, with a current of 2 mph? Here is Sam rowing 4 mph on the lake:

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3. When Sam gets to the river and paddles upstream, the current is working against him, and as a result he will move at a slower pace. Think of his rate as the rate of a person walking along the bank keeping pace with the canoe. Here is Sam paddling upstream:

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5. When Sam paddles upstream, his rate is: Sam’s rate going upstream is 2 mph. Someone walking on the bank at 2 mph would stay right with the canoe.

6. Again, think of his rate as the rate of a person walking along the bank keeping pace with the canoe. Here is Sam paddling downstream: When Sam paddles downstream, the current is helping him, and as a result he will move at a faster pace.

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8. When Sam paddles downstream, his rate is: Sam’s rate going downstream is 6 mph. Someone walking on the bank at 6 mph would stay right with the canoe.

9. Example 2: Mary’s motorboat can go x miles per hour on a lake. What will her rate be when she takes her boat: a) up a river, against a current of y mph? b) down a river, with a current of y mph?

10. a) Up river: Going up river, Mary’s boat can go x – y mph. b) Down river: Going down river, Mary’s boat can go x + y mph.