Question

A boat takes two hours to travel 8km down and 8km up the river when the water is still. How much time will the boat take to make the same trip when the river starts flowing at 4kmph?
A) 2 hour
B) 2 hours 40 minute
C) 3 hour
D) 3 hours 40 minute

Answer 1

Hint: The way of measuring how quickly an object is moving or being done is called speed. The measurement of how far the object is or travelled is called distance. The time which a clock reads. The quantity of the time is scalar.

Formula used:
To solve this type of question we use the following formula.
$\text{Speed} = \dfrac{\text{distance}}{\text{time}}$


Complete step by step answer:
Let us first write the information given in the question.
To travel 8km up and 8km down when water is still 2 hours are taken by the boat, speed of river = 4 km/h.
Now, we have to calculate the time taken when the river starts flowing with a speed of 4km/h.
So we can write the speed of the boat in still water as below.
$ {v_{\text{boat-stillwater}}} = \dfrac{{\text{total distance}}}{{\text{time taken}}}$
$ = \dfrac{{16}}{2}$
$ = 8km/s$
Now, when the river starts flowing with a speed $4km/h.$
When the boat travels downstream the speed of the boat is given below.
${v_{\text{boat-downstream}}} = 8km/h + 4km/h$
$ = 12km/h$
Now let us calculate the time taken by the boat to travel downstream.
${t_{\text{down-stream}}} = \dfrac{\text{distance}}{\text{time}}$
$ = \dfrac{8}{{12}} = \dfrac{2}{3}h$ ……... (1)
When the boat travels upstream the speed of the boat is given below.
${v_{\text{boat-upstream}}} = 8km/h - 4km/h$
$ = 4km/h$
Now let us calculate the time taken by the boat to travel upstream.
${t_{\text{up-stream}}} =\dfrac{\text{distance}}{\text{time}}$
$= \dfrac{8}{4} = 2h$ …... (2)
Therefore, the total time taken by the boat is the sum of equation (1) and (2).
$t = \dfrac{2}{3} + 2$
$ = \dfrac{8}{3}h = 2h40\min $

$\therefore $ The boat will take 2hour 40 mins to complete the trip. Hence option (B) is correct.

Note:
- When the boat travels in the direction of the flow of the river then it’s easy for the boat to move. In this condition, the effective speed of the boat is the total of both speeds of the boat and the speed of the river. Hence effective speed increases.
- Similarly, when a boat travels in the direction opposite the flow of the river then it’s difficult for the boat to move. In this condition, the effective speed of the boat is the difference between both speeds of the boat and the speed of the river. Hence effective speed decreases.