A river flows with a uniform velocity vr. A person in a motorboat travels 1.13 k

Question

A river flows with a uniform velocity vr. A person in a motorboat travels 1.13 km upstream, at which time she passes a log floating by. Always with the same engine throttle setting, the boater continues to travel upstream for another 1.42 km, which takes her 62.2 min. She then turns the boat around and returns downstream to her starting point, which she reaches at the same time as the same log does.

1) How much time does the boater spend traveling back downstream?

2) Calculate the speed of the river.

3) Calculate the boat's speed relative to the water

I felt like I had the answer but after submitting it in several different ways, it said I still has the wrong answer. For the third question I tried the answer of .0228 km/min and I also tried ~.38 m/s, but they both didn't work. If someone could show me the correct way of getting the answers that would be great.

Explanation / Answer

Let v be the speed of the speedboat.

Time to travel upstream=(1.13+1.42)/(v-vr)=62.2min

Time to return to starting point=(1.13+1.42)/(v+vr)=1.13/vr

Solving simultaneously,

v=0.20km/min

vr=0.16km/min

1)Time to travel downstream=(1.13+1.42)/(v+vr)=(1.13+1.42)/(0.2+0.16)=7.08 min

2)vr=0.16km/min=160/60m/s=2.67m/s

3)v=0.20km/min=200/60 m/s=3.33m/s

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