Question

A boat takes a circular route to travel a total distance of 24km to reach its initial position. The speed of the boat in still water is 5km/hr and the speed of the stream is 3km/hr. How much time(in hours) does the boat travel upstream and downstream respectively

Answer 1

5_3=2kmper hr travel in 1 hr
so it compete in 12 hr

Answer 2

The boat takes 12 hours and 3 hours to travel upstream and downstream respectively.

Given,

Distance that needs to be covered, D=24 km

Speed of the boat in still water, Vb=5 km/h

Speed of the stream(river flow), Vr=3 km/h.

To find,

the time(in hours) taken for the boat to travel upstream and downstream respectively.

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.

First case:The boat goes upstream to travel 24 km.

$Vnet=V1-V2\\Vnet=Vb-Vr\\Vnet=(5-3) km/h\\Vnet=2 km/h.$

The resultant speed of the upstream motion is 8 km/h.

$Speed=\frac{Distance}{Time} \\Vnet=\frac{D}{Time} \\2=\frac{24}{Time}\\ Time=\frac{24}{2} \\Time=12 hours.$

Second case:The boat goes downstream to travel 24 km.

$Vnet=V1+V2\\Vnet=Vb+Vr\\Vnet=(5+3) km/h\\Vnet=8 km/h.$

The resultant speed of the downstream motion is 2 km/h.

$Speed=\frac{Distance}{Time} \\Vnet=\frac{D}{Time} \\8=\frac{24}{Time}\\ Time=\frac{24}{8} \\Time=3 hours.$

Time taken in upstream motion is 12 hours and time taken in downstream motion is 3 hours.

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