A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is
Answers
Solution
- Total time taken would be 8/3 hrs
Given
- Total Time Taken in still water (T) = 2 hours
- Total Distance (S) = 16 Km
- Velocity of water = 4 km/h
To finD
- Time taken during the whole journey
Now,
Velocity of the Boat :
Upstream
While going upstream,the water current is opposite to the motion of boat,their velocities are subtracted :
Downstream
Velocity of the water and boat are in the same direction
Total Time
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- Total Distance travelled
= 8km+8km = 16km
- Time taken to travel 16km = 2hours
- Velocity of water=4km /h
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Total Time taken to travel 8km upstream and 8km downstream =?
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Let,
speed of boat in still water = x km/hr
Speed of water = y km/ hr
given speed of water =4km/ hr
★Thus y= 4km/hr--------(i)
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Now it's given,
The boat goes 16km in 2hours
thus it's velocity in still water is:
★Thus x= 8km/hr---------(ii)
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The velocity of the boat in upstream = (x-y)km/ hr
》The velocity in upstream
= (8-4) km/hr ( from i and ii,x=8 and y=4)
= 4km/hr
Time taken by the boat to cover 8km upstream is:
Thus,
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Velocity of boat in downstream is
=(x+y)km/hr
=(8+4)km/hr (from i and ii)
=12km/hr
Time taken by the boat to cover 8km downstream is:
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Thus total time taken
= Time taken to go upstream+ Time taken to go downstream
=2 hour+ 40 minutes
=2hour 40 minutes
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