Question : The speed of a boat in still water is 15 km/hr, and the speed of the current is 5 km/hr. In how much time (in hours) will the boat travel a distance of 60 km upstream and the same distance downstream?
Option 1: 20
Option 2: 12
Option 3: 9
Option 4: 10
Correct Answer: 9
Solution :
Given,
The speed of a boat in still water is 15 km/hr
The speed of the current is 5 km/hr
Distance of upstream or downstream = 60 km
We know,
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
Also, If the speed of the boat is $x$ km/hr, and the speed of the stream is $y$ km/hr then,
Speed of boat upstream = $(x - y)$ km/hr
Speed of boat downstream = $(x + y)$ km/hr
According to the question:
⇒ $\frac{D}{(x - y)} + \frac{D}{(x +y)} = T$
⇒ $\frac{60}{15 - 5} + \frac{60}{15 + 5} = T$
⇒ $T = \frac{60}{10} + \frac{60}{20}$
⇒ $T = 6 + 3$
⇒ $T = 9$ hours
Hence, the correct answer is 9.
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