Question

A boat takes 4 hours travelling upstream to reach point B from point A. If the velocity of the boat in still water is 4km/hr and the velocity of the stream is 2km/hr, then find the distance between A and B.
[a] 4km
[b] 5km
[c] 6km
[d] 8km

Answer 1

Hint: Assume that the distance between A and B is x. Use the fact that if the speed of the boat in still water is x and the speed of the water of the stream is y, then the velocity of the boat upstream is x-y. Hence find the velocity of the boat upstream. Use the fact that the time taken to cover the distance D with speed S is given by $T=\dfrac{D}{S}$. Hence form an equation in x. Solve for x and hence find the distance between A and B. Verify your answer.

Complete step-by-step answer:
Let the distance between A and B is x.

Velocity of the boat in still water = 4km/hr
Velocity of the stream = 2Km/hr
Time taken to cover the distance AB = 4 hours
We know that if the speed of the boat in still water is x and the speed of the water of the stream is y, then the velocity of the boat upstream is x-y.
Hence, we have
The velocity of the boat upstream $=4-2=2$
Now, we know that the time taken to cover the distance D with speed S is given by $T=\dfrac{D}{S}$.
Hence, we have
$4=\dfrac{x}{2}$
Multiplying both sides by 2, we get
$x=2\times 4=8$
Hence the distance between AB = 8km.
Hence option [d] is correct.

Note: Alternative Solution:
We can also solve the above question using the fact that for every 1 hr the distance covered by the boat will be 2km less than what the boat will have covered in still water.
Hence in 1 hour the boat covers 4-2 = 2km distance
Hence the distance covered by the boat in 4 hours $=2\times 4=8$
Hence the distance between AB is 8km, which is the same as obtained above.
Hence option [d] is correct.