A boat can go 5 km upstream and $7 \frac{1}{2}$ km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km downstream?
Answer & explanation
Correct answer: option 2
We know that,
Upstream speed = Speed of the boat in still water - Speed of flow of the stream
Downstream speed = Speed of the boat in still water + Speed of flow of the stream
We have,
A boat goes 5 km upstream and 7.5 km downstream in 45 minutes
Also, it goes 5 km downstream and 2.5 km upstream in 25 minutes
According to the question,
Let the Downstream and Upstream speed be 'd' km/hr and 'u' km/hr respectively
As per the question,
5/u + 7.5/d = 45/60 -----eq-n(1)
2.5/u + 5/d = 25/60 -----eq-n(2)
Multiplying eq-n(2) by 2 and then subtracting eq-n(1) from (2), we get
2.5d = 560
⇒ d = 30
By putting the value of 'd' in any of the eq-n, we get the value of 'u'
⇒ u = 10
Now
Time is taken to travel 6 km downstream = 6/30 hour or 12 minutes