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?

12

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