A river flows with a uniform velocity v r . A person in a motorboat travels1.29

Question

A river flows with a uniform velocityvr. A person in a motorboat travels1.29 km upstream, at which time she passes a log floating by.Always with the same engine throttle setting, the boater continuesto travel upstream for another 1.35 km, which takes her 56.3 min.She then turns the boat around and returns downstream to herstarting point, which she reaches at the same time as the same logdoes. How much time does the boater spend travelingback downstream? Calculate the speed of theriver.Calculate the boat's speed relative to thewater.

Explanation / Answer

There are 3 time periods. The boat passed thelog at the end of t1. A key point to note, and use, is that thetime from the first sighting of the log to the second sighting isthe same for the boat and for the log. Ttotal = t1 + t2 + t3
where t1 is the time it took the boat to go the first 1.29 km, t2is the time from the first log sighting to the boat's most upstreampoint, and t3 is the time from the boat's most upstream point tothe return to the starting point. We know that t2=56.4 min.

The boat's water speed is
Vb = 1.29 km / t1 so
t1 = 1.29 km / vb

We can get vb from the given info about time period t2.
vb = 1.35 km / 56.3 min = .02398 km/min
That's answer #3.
So we can get t1
t1 = 1.29 km / .02398 km/min = 52.82 min

By the start of time period t3, the boat is
1.29 km + 1.35 km = 2.64 km upstream from the starting point.

The log's travel time, t2+t3, is
t2+t3 = 1.29 km / vr
We also know that
t2+t3 = 2.64 km / vb = 2.64 km / (.02398 km/min) = 110.1 minThat's answer #1.

And you can get answer #2 from
t2+t3 = 1.29 km / vr Once again check my math. The formulas shouldbe correct. You may have to convert your answers from minutes toseconds which is a matter of dividing by 60. Thanks pleaserate.

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