Question

Stewart decided to take a trip down the the river in his kayak. He traveled 31 miles in 4 hours going down stream on the river. He then turned around to try to paddle back upstream but only made it 10.5 miles and quit after 2 hours and had someone pick him up via car because he was getting too tired. What is the speed at which Stewart rows in still water? What is the speed of the river?

Answer 1

Stewart's rowing speed in still water is 6.5 miles per hour, and the river flows at 1.25 miles per hour. These speeds are found by creating equations based on the distances traveled and times taken going downstream and upstream, then solving those equations simultaneously.

Step-by-step explanation:

To determine the speed at which Stewart rows in still water and the speed of the river, we can set up two equations using the information provided. Let v represent the speed of the kayak in still water and r represent the speed of the river.

Going downstream, the effective speed is v + r because the river speed adds to Stewart's rowing speed. The distance covered is 31 miles in 4 hours, giving us the equation:

1. (v + r) × 4 = 31

When Stewart turns around to paddle back upstream, the effective speed is v - r because the river is working against him. He made it 10.5 miles in 2 hours, which gives us a second equation:

1. (v - r) × 2 = 10.5

Solving these two equations simultaneously, we get:

1. Divide the first equation by 4: v + r = 7.75
2. Divide the second equation by 2: v - r = 5.25
3. Add the two resulting equations to eliminate r and find v: 2v = 13, so v = 6.5 miles per hour
4. Substitute the value of v in any of the above two equations to find r: 6.5 + r = 7.75, so r = 1.25 miles per hour

Therefore, Stewart rows at 6.5 miles per hour in still water, and the river flows at 1.25 miles per hour.