A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. a. Write an equation for the rate of the canoe downstream. b. Write an equation for the rate of the canoe upstream. c. Solve the system to find the family’s paddling speed in still water. d. Find the speed of the current of the river.

Question

A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank.  a. Write an equation for the rate of the canoe downstream.  b. Write an equation for the rate of the canoe upstream.  c. Solve the system to find the family’s paddling speed in still water.  d. Find the speed of the current of the river.

Daphne Broadhurst · Accepted Answer

Let x be the paddling speed in still water and y be the speed of the current of the river, both in mi/h.a)Downstream, we add the paddling speed in still water and the speed of the current of the river:&amp;nbsp;x+y=2.75b)Upstream, we subtract the paddling speed in still water and the speed of the current of the river:&amp;nbsp;x−y=1.5c)Add each side of (1) and (2) to eliminate y and solve for x:&amp;nbsp;2x=4.25x=2.125In still water, the paddling speed is 2.125 miles per hour.d)Subtract each side of (1) and (2) to eliminate x and solve for y:&amp;nbsp;2y=1.25y=0.625Thus, the speed of the current of the river is 0.625 mi/h

A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they pa

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