# Boats and Streams

1. A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

A. 1 km/hr

B. 1.5 km/hr

C. 2 km/hr

D. 2.5 km/hr

Explanation:

Suppose he move 4 km downstream in x hours.
Then, Speed downstream = ( 4 / x ) km/hr
Speed upstream = (3 / x ) km/hr
Therefore, 48 / ( 4 / x ) + 48 / ( 3 / x ) = 14 or x = 1/2
So, Speed downstream = 8 km/hr
Speed upstream = 6 km/hr
Rate of the stream = (8-6)/2 km/hr = 1 km/hr

2. A man takes twice as long to row up the stream as to row down the stream. The ratio of the speed of the boat (in still water) to the stream is:

A. 2 : 1

B. 3 : 1

C. 3 : 2

D. 3 : 5

Explanation:

Let upstream speed be x kmph.
Then, downstream speed = 2x kmph.

Speed of boat in still water = 1/2(x + y)
Speed of stream = 1/2(x - y)

Therefore , (Speed of boat in still water) : (Speed of stream)
= ( 2x + x) /2 : ( 2x - x) /2
= 3x / 2 : x /2
= 3 : 1

3. Speed of a boat in still water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

A. 16 hours

B. 18 hours

C. 20 hours

D. 24 hours

Explanation:

Distance = 105 km
Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
Total time taken = Distance / Speed upstream + Distance/ Speed downstream
= ( 105 / 7.5) + (105 / 10.5 ) hours
= 14 + 10
= 24 hours.
Total time taken by him = 24 hours.

4. A boatman goes 2 km upstream in 1 hour and goes 1 km downstream in 10 minutes. How long will it take to go 5 km in still water ?

A. 40 minutes

B. 1 hour

C. 1 hr 15 min

D. 1 hr 30 min

Explanation:

Downstream speed = ( 1 / 10 x 60 ) km/hr = 6 km/hr
Upstream speed = 2 km/hr
Speed in still water = 1/2 * (6 + 2) km/hr = 4 km/hr.
Therefore, Required time = ( 5/4 ) hrs = 1 ( 1/4 ) hrs = 1 hr 15 min.

5. A boat covers a certain distance downstream in 1 hour, while it comes back upstream in 1 1/2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

A. 12 kmph

B. 13 kmph

C. 14 kmph

D. 15 kmph

Explanation:

Let the speed of the boat in still water be x kmph.
Given,speed of the stream = 3 kmph

Then, Speed downstream = speed of the boat + speed of the stream
= (x + 3) kmph

Speed upstream = speed of the boat - speed of the stream
= (x - 3) kmph.

Therefore, Downstream distance = upstream distance
=> Speed Downstream * Downstream Time = Speed upstream *upstream Time
=> (x + 3) x 1 = (x - 3) x 3/2
=> 2x + 6 = 3x - 9
=> x = 15 kmph.
Thus, speed of the boat in still water = 15 kmph