a motorboat goes downstream in the river and covers the distance between two coastal towns in 3 hours. It covers this distance upstream in 4 hours. If the speed of the stream is 5 km/hr , find the speed of the boat in still water and the distance between the two coastal towns
Answers
Answer:
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 = 6x – 12
⇒ 5x – 6x = –12 – 10
∴ –x = –22
x = 22.
Therefore speed of the boat in still water is 22 kmph.