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KAYAKING

During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream (with the current), as shown. The speed of the current remained constant during the trip. Find the average speed of the kayak in still water and the speed of the current. EXAMPLE 4.

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KAYAKING

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  1. During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream (with the current), as shown. The speed of the current remained constant during the trip. Find the average speed of the kayak in still water and the speed of the current. EXAMPLE 4 Write and solve a linear system KAYAKING

  2. Upstream: Downstream: 12 =r 3 12 =r 2 d = rt d =rt EXAMPLE 4 Write and solve a linear system STEP1 Write a system of equations. First find the speed of the kayak going upstream and the speed of the kayak going downstream. 4 =r 6 =r

  3. Going upstream Equation 1: – y x = 4 EXAMPLE 4 Write and solve a linear system Use the speeds to write a linear system. Let xbe the average speed of the kayak in still water, and let ybe the speed of the current.

  4. Equation 2: Going downstream x 6 y = + EXAMPLE 4 Write and solve a linear system

  5. x + y = 6 EXAMPLE 4 Write and solve a linear system STEP2 Solve the system of equations. x –y = 4 Write Equation 1. Write Equation 2. 2x = 10 Add equations. x = 5 Solve forx. Substitute 5 for xin Equation 2 and solve for y.

  6. EXAMPLE 4 Write and solve a linear system 5 + y = 6 Substitute 5 for xin Equation 2. y = 1 Subtract 5 from each side.

  7. ANSWER average speed of the kayak: 3.5 mi/h, speed of the current 1.5 mi/h for Example 4 GUIDED PRACTICE 7. WHAT IF?In Example 4, suppose it takes the kayaker 5 hours to travel 10 miles upstream and 2 hours to travel 10 miles downstream. The speed of the current remains constant during the trip. Find the average speed of the kayak in still water and the speed of the current.

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