A motor boat goes downstream in a river, covers the distance between two coastal towns in 5 hours. It covers same distance upstream in six hours. The speed of water is 2 km/h find the speed of the motor boat in still water.
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Since we have to find the speed of the boat in still water, let us suppose that it is x km/h.
This means that while going downstream the speed of the boat will be (x+2) kmph because the water current is pushing the boat at 2 kmph in addition to its own speed 'x' kmph.
Now the speed of the boat down stream =(x+2) kmph
⇒ distance covered in 1 hour =x+2 km
∴ distance covered in 5 hours =5(x+2) km
Hence the distance between A and B is 5(x+2)km
But while going upstream the boat has to work against the water current.
Therefore its speed upstream will be (x−2) kmph.
⇒ Distance covered in 1 hour =(x−2) km
Distance covered in 6 hours =6(x−2) km
∴ distance between A and B is 6(x−2) km
But the distance between A and B is fixed
∴ 5(x+2)=6(x−2)
⇒ 5x+10=−12−10
∴ −x=−22
x=22
Therefore speed of the boat in still water is 22 kmph.
Step-by-step explanation:
Since we have to find the speed of the boat in still water, let us suppose that it is x km/h.
This means that while going downstream the speed of the boat will be (x+2) kmph because the water current is pushing the boat at 2 kmph in addition to its own speed 'x' kmph.
Now the speed of the boat down stream =(x+2) kmph
⇒ distance covered in 1 hour =x+2 km
∴ distance covered in 5 hours =5(x+2) km
Hence the distance between A and B is 5(x+2)km
But while going upstream the boat has to work against the water current.
Therefore its speed upstream will be (x−2) kmph.
⇒ Distance covered in 1 hour =(x−2) km
Distance covered in 6 hours =6(x−2) km
∴ distance between A and B is 6(x−2) km
But the distance between A and B is fixed
∴ 5(x+2)=6(x−2)
⇒ 5x+10=−12−10
∴ −x=−22
x=22
Therefore speed of the boat in still water is 22 kmph.