A boat takes 16 minutes and 24 minutes to cover a certain distance downstream and upstream, respectively. If the speed of the boat in still water is 15 km/h, find the speed of the stream.
Answer & explanation
Correct answer: option 2
We know that,
Upstream Speed = Speed of Boat – Speed of current
Downstream Speed = Speed of Boat + Speed of current
Given,
A boat takes 16 minutes and 24 minutes to cover a certain distance downstream and upstream, respectively.
The speed of the boat in still water = 15 km/h.
Let the distance be D and the speed of the stream be S km/h.
Upstream speed = (15 - S) km/h
Downstream speed = (15 + S) km/h
According to the concept,
\(\frac{D}{15 + R}\) = \(\frac{16}{60}\)
D = \(\frac{240 + 16D}{60}\)----(A)
And,
\(\frac{D}{15 - R}\) = \(\frac{24}{60}\)
D = \(\frac{360 - 16D}{60}\)----(B)
From A and B,
= 240 + 16D = 360 - 24D
= 40D = 120
= D = 3