When the boat is going upstream (against the current), the boat is being slowed down by the current so that The speed of the boat in still water minus The speed of the current T T T T T The speed of the boat x y going upstream 47) It takes 5 hours for a boat to travel 80 miles downstream. The boat can travel the same distance back upstream in 8 hours. Find the speed of the boat in still water and the speed of the current. speed of boat in still water: 13 mph; speed of the current: 3 mph 48) A boat can travel 12 miles downstream in 1.5 hours. It takes 3 hours for the boat to travel back to the same spot going upstream. Find the speed of the boat in still water and the speed of the current. speed of boat in still water: 6 mph; speed of the current: 2 mph 49) A jet can travel 1000 miles against the wind in 2.5 hours. Going with the wind, the jet could travel 1250 miles in the same amount of time. Find the speed of the jet in still air and speed of the wind. speed of jet in still air: 450 mph; speed of the wind: 50 mph 50) It takes 2 hours for a small plane to travel 390 miles with the wind. Going against the wind, the plane can travel 330 miles in the same amount of time. Find the speed of the plane in still air and the speed of the wind. speed of plane in still air: 180 mph; speed of the wind: 15 mph The speed of the boat going upstream Use this idea to solve Exercises 45–50. 45) It takes 2 hours for a boat to travel 14 miles downstream. The boat can travel 10 miles upstream in the same amount of time. Find the speed of the boat in still water and the speed of the current. (Hint: Use the information in the following table, and write a system of equations.) speed of boat in still water: 6 mph; speed of the current: 1 mph d r t Downstream 14 x y 2 Upstream 10 x y 2 46) A boat can travel 15 miles downstream in 0.75 hours. It takes the same amount of time for the boat to travel 9 miles upstream. Find the speed of the boat in still water and the speed of the current. (Hint: Use the information in the following table, and write a system of equations.) speed of boat in still water: 16 mph; speed of the current: 4 mph d r t Downstream 15 x y 0.75 Upstream 9 x y 0.75 R3) Did you check your answers by hand before looking at the answers in the back of the book? R4) Choose six problems and redo them without looking back at the book or your notes for help. Were you able to do them on your own? R1) If you have two unknowns in an application problem, how many equations do you need to solve the problem? R2) In which of your future courses do you think you will need to solve a system of linear equations? www.mhhe.com/messersmith SECTION 4.4 Applications of Systems of Two Equations 285
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