Question

A boat must get from point A to point B on the opposite bank of the river moving along a straight line AB that makes 120 degree angle with the flow direction. If distance AB is 2.5 km, the speed of boat in still water is 7 km/hr and the speed of the river current is 3 km/hr, then the minimum travel time of the boat is?

Answer 1

Explanation:

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Answer 2

The minimum travel time of the boat is 0.42hr.

Given:-

Angle with flow direction = 120°

Width of the river = 2.5km

Speed of boat in still water = 7km/hr

Speed of river current = 3km/hr

To Find:-

The minimum travel time of the boat.

Solution:-

We can easily find out the minimum travel time of the boat by using these simple steps.

As

Angle with flow direction = 120°

Actual angle (a) = 120-90 = 30°

Width of the river (d) = 2.5km

Speed of boat in still water (vbr) = 7km/hr

Speed of river current = 3km/hr

Minimum time required (t) =?

Here, speed of river current has no use, because for minimum time speed of river current is taken as zero.

According to the formula of time taken by boat in water,

$t = \frac{d}{vbr \cos(a) }$

on putting the values, we get

$t = \frac{2.5}{7 \times \cos(30) }$

$t = \frac{25 \times 2}{70 \times \sqrt{3} }$

$t = \frac{50}{70 \times \sqrt{3} }$

$t = \frac{5}{7 \times \sqrt{3} }$

ok solving we get,

$t = 0.42hr$

Hence, The minimum travel time of the boat is 0.42hr.

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