Question

A boat takes 2 hours to go 8 km and come back to a still water lake. With velocity of 4 km/hr the time taken for going upstream 8 km and going back is
A 140 minutes
B 150 minutes
C 160 minutes
D 170 minutes

Answer 1

Hint: As the boat goes to 8 km and comes back so we have to add both distances one for going and another is for coming and then use the proper formula for speed, distance and time.

Complete step-by-step answer: It is given that the boat goes 8 km and comes back in still water and it takes 2 hours for this. So we first find the velocity of boat Vb
As velocity is distance covered by the boat per unit time,
Distance covered by boat in 2 hours is = 16
Therefore, velocity of boat is
⇒ ${V_b} = \dfrac{{8 + 8}}{2} = \dfrac{{16}}{2} = 8km/hr$
And velocity of water is Vw = 4km/hr
Now, time taking in going upstream is distance covered by boat in going 8 km divided by the velocity of upstream and upstream velocity is the difference of the velocities of boat and water
⇒ Time taken for going upstream is ${t_1} = \dfrac{8}{{{V_b} - {V_w}}} = \dfrac{8}{{8 - 4}} = 2hr = 2 \times 60\min = 120\min $
Now, Time taken by boat in going downstream is distance covered by boat in going 8 km back divided by the speed of downstream and speed of downstream is the sum of the velocity of the boat and velocity of water
⇒ Time taken for going downstream is ${t_2} = \dfrac{8}{{{V_b} + {V_w}}} = \dfrac{8}{{8 + 4}} = \dfrac{8}{{12}}hr = \dfrac{8}{{12}} \times 60\min = 140\min $
As the water helps the motion of boat then total time taken by boat is sum of time taken by boat to go upstream and the time taken by boat to go downstream
⇒ Total time taken by boat is $t = {t_1} + {t_2} = 120 + 40 = 160\min $

Hence, C option is correct.

Note: Here keep in mind that when the boat is going downstream the boat opposes the velocity of water so we add there velocities and while going upstream then water and boat are in the same direction so we take the difference between there velocities.