Question

A boat goes $ 40\;km $ upstream in $ 8 $ hours and $ 36\;km $ downstream in $ 6 $ hours. Then what is the speed of the boat in still water?
A. $ 6.5{\text{ km/hr}} $
B. $ 5.5{\text{ km/hr}} $
C. $ 6\;{\text{km/hr}} $
D. $ 5{\text{ km/hr}} $

Answer 1

Hint: As we know that the speed is equal to the distance travelled upon the time taken. Here we are given distance and the time taken for upstream and the downstream of the water, so will find individual speed and then the average speed for the required speed in still water.

Complete step-by-step answer:
Here first of all we will find the average of the speed.
Given that a boat goes $ 40\;km $ upstream in $ 8 $ hours.
Therefore, Speed $ = \dfrac{{40}}{8} $
Find the common factors in the numerator and the numerator and simplify.
Speed $ = \dfrac{{8 \times 5}}{8} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
Speed $ = 5\;{\text{km/hr}} $ ... (A)
Also, given that $ 36\;km $ downstream in $ 6 $ hours.
Therefore, Speed $ = \dfrac{{36}}{6} $
Find the common factors in the numerator and the numerator and simplify.
Speed $ = \dfrac{{6 \times 6}}{6} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
Speed $ = 6\;{\text{km/hr}} $ ... (B)
Therefore, the speed of the boat in still water is the average of the speeds.
By using the equation (A) and (B)
Speed $ = \dfrac{{6 + 5}}{2} $
Simplify the above equation –
Speed $ = \dfrac{{11}}{2} $
Divide and simplify –
Speed $ = 5.5\;{\text{km/hr}} $
So, the correct answer is “Option B”.

Note: Be careful while taking the average of the speeds, since here both the speeds were in the same system of units it was easy to substitute. Always check the given units and before placing values just check that all the units should be in the same system.