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A motorboat has two throttle positions on its engines.the high speed position propels the boat at 30km/hr in still water and the low speed position gives one third the higher speed. the boat moves from its dock downstream on a river with throttle at low speed position . the return trip took 5% longer time that it did for the downstream trip.Determine the velocity of the flow of the river.

A motorboat has two throttle positions on its engines.the high speed position propels the boat at 30km/hr in still water and the low speed position gives one third the higher speed. the boat moves from its dock downstream on a river with throttle at low speed position . the return trip took 5% longer time that it did for the downstream trip.Determine the velocity of the flow of the river.

Grade:10

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
The low speed velocity would be given by
\frac{1}{3}\times 30=10 km/hr
Let the speed of the river be vr.
Hence the net downward speed would be:v_{r}+10and the net upstream speed will be equal to10-v_{r}.
Let the downstream/upstream distance be equal to d.
Hence, the time taken while going downstream would be equal to:\frac{d}{10+v_{r}}and the time taken while going upstream would be equal to:\frac{d}{10-v_{r}}
Hence,\frac{d}{10-v_{r}}=1.05\frac{d}{10+v_{r}}
Therefore,
{10+v_{r}}=1.05({10-v_{r}})
v_{r}+1.05v_{r}=1.05\left ( 10-1 \right )=9\times 1.05=9.45\Rightarrow v_{r}=\frac{9.45}{2.05}=4.61 km/hrRegards
Sumit

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