a motorboat goes down stream in a river and covers the distance between two coastal town in 5 hours it covers this distance upstream in 6 hours if the speed of the stream is 2 kilometres / hour find the speed of the boat in still water
Answers
Given:-
- The time taken to cover distance between the coastal towns by upstream is 6km/hr and by downstream is 5km/hr.
- Speed of the water is (y) = 4km/hr
Let the distance between two coastal towns be D
case1: through upstream speed
D = (x-4) × 6 --(1)
case2: through downstream speed
D = (x+4) × 5 --(2)
From equation (1) and (2)
(x-4) × 6 = (x+4) × 5
6x – 24 = 5x + 20
6x - 5x = 20 + 24
x = 44
From equation (1)
d = (44-4) × 6
= 40 × 6
= 240
@WildCat7083
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.