Question

speed of a boat in still water is 4km/ h it is moving along the direction of river flow between two fixed points when boat goes in downstream it takes 10minute and it takes 30minute when goes in upstream direction what is speed of river flow​

Answer 1

Answer:

2km/hr is the speed of river flow

Answer 2

River flows with a speed of 2 km/h.

Given,

Speed of the boat in still water, Vb=4 km/h

Time taken when it moved downstream=10 minutes

Time taken when it moved upstream=30 minutes.

To find,

the speed of the river flow, Vr.

Solution:

• In an upstream motion, the resultant speed of the motion is equal to the difference of the individual speeds of the components present in the motion.
• Vnet=|V1-V2|.
• In a downstream motion, the resultant speed of the motion is equal to the sum of the individual speeds of the components present in the motion.
• Vnet=V1+V2.

Let the speed of the river flow be Vr.

First case:The boat goes downstream and takes 10 minutes(1 hour=60 minutes).

$Vnet=Vb+Vr\\Vnet=(4+Vr) km/h.$

The resultant speed in the downstream motion is (4+Vr) km/h.

Let the length of the river D.

$Speed=\frac{Distance}{Time} \\(4+Vr)=\frac{D}{\frac{10}{60} } \\(4+Vr)=\frac{D}{\frac{1}{6} } \\(4+Vr)=6D\\D=\frac{(4+Vr)}{6}km .$      

Second case:The boat goes upstream and takes 30 minutes(1 hour=60 minutes).

$Vnet=Vb-Vr\\Vnet=(4-Vr)km/h.$

$Speed=\frac{Distance}{Time} \\(4-Vr)=\frac{D}{\frac{30}{60} } \\(4-Vr)=\frac{D}{\frac{1}{2} } \\(4-Vr)=2D\\D=\frac{(4-Vr)}{2}km .$    

As the distance D is same,

$\frac{(4+Vr)}{6} =\frac{(4-Vr)}{2} \\\frac{(4+Vr)}{3}=(4-Vr)\\(4+Vr)=3(4-Vr)\\4+Vr=12-3Vr\\3Vr+Vr=12-4\\4Vr=8\\Vr=2 km/h.$

The speed of the river flow is 2 km/h.

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