Question

For going 60km down stream and coming back a boat takes 9 hours
If the speed of the boat in still water is 15 km/hr. Find the speed of current water.

Answer 1

Answer:Let the speed of boat in still water = u km/h

And speed of the stream = v km/h. Please remember u needs to more than v, otherwise the answers would be funny.

Now when the boat is going downstream, its effective speed becomes = (u + v ) km/h; and

when the boat is going upstream, its effective speed becomes = (u - v) km/h

Now in accordance with the statement of the question, we have;

4 (u + v) + 3 (u - v) = 116;

==>4 u +4 v +3 u -3 v = 116; ==> 7 u + v = 116——(1)

and

3 (u +v) + 4 (u -v ) =108; ==> 3 u + 3 v +4 u - 4 v =108

==> 7 u - v = 108 —(2)

Adding eqns (1) and (2), we get

14 u = 224; ==> u = 16 km/h

And substituting for u in eq(1) we get;

v = 4 km/h

So speed of boat in still water = 16 km/h

And speed of stream = 4 km/h

Verification:

Effective speed of boat when going downstream = (16 +4) km/h = 20 km/h

Effective speed of boat when going upstream = (16 -4 ) km/h = 12 km/h

So, we have in first case

4 × 20 + 3 × 12 = 80 + 36 = 116 km

And in second case

3 × 20 + 4 × 12 = 60 + 48 = 108 km

So our results agree with the statement in both cases.

Step-by-step explanation: