Boats and Streams with Explanation

Q1. A boat travelling along the stream covers 16 km in 2 hours. It covers the same distance against the stream in 4 hours. Find the speed of the boat in still water?

Answer- Option A

Explanation-

Rate downstream =

16 2

kmph

=

8 kmph

Rate upstream =

16 4

kmph

=

4 kmph

Speed in still water =

1 2

(8 + 4) kmph

=

6 kmph

Q2. A man rows 1 km downstream in 10 minutes and runs 2 km upstream in 1 hour. How much time will he take to go 5 km in still water?

Answer- Option D

Explanation-

Rate downstream =

1 10

x

60

kmph

=

6 kmph

Rate upstream = 2 kmph
Speed in still water =

1 2

(6 + 2) kmph

=

4 kmph

Required time =

5 4

hrs

=

1 hr 15 min

Q3. The speed of a motorboat going against the stream is 8 km/hr, and the speed of the stream is 2 km/hr. Determine the speed of the motorboat in downstream?

Answer- Option C

Explanation-

Let the speed of a motorboat in still water be x km/hr.
Given, Speed upstream = 8 km/hr = (x - 2) km/hr
x = 10 km/hr
Speed downstream = (x + 2) kmph = 12 kmph

Q4. A boat takes 4 hours to cover a certain distance running downstream, while it requires 8 hours 48 minutes to cover the same distance. Find the ratio between the speed of the current and the speed of the boat?

Answer- Option B

Explanation-

Let the speed of the boat and stream be x km/hr and y km/hr.
Speed downstream = (x + y) miles/hr
Speed upstream = (x - y) miles/hr

4(x + y)

=

8

+

48 60

(x - y)

5x + 5y = 11x - 11y

y x

=

3 8

Q5. A paddleboat can row at 13 km/hr in still water. Find the time taken by the paddleboat to travel 68 km along the stream, if the speed of the stream is 4 km/hr.

Answer- Option A

Explanation-

Speed downstream = (13 + 4) km/hr = 17 km/hr
Time taken to travel 68 km downstream =

68 17

hrs

=

4 hrs

Q6. The time taken by a man to travel 36 miles downstream is 90 minutes less than to go the same distance upstream. The speed of the man in still water is 10 mph. Find the speed of the stream?

Answer- Option C

Explanation-

Let the speed of the stream be x miles/hr.
Speed downstream = (10 + x) miles/hr
Speed upstream = (10 - x) miles/hr

36 (10 + x)

=

36 (10 - x)

-

90 60

x² + 48x - 100 = 0
(x + 50)(x - 2) = 0
x = 2 mph

Q7. A man takes 50 minutes to go to a place and come back. If his speed in still water is 7.5 km/hr and the river is running at 1.5 km/hr, what is the distance of that place?

Answer- Option D

Explanation-

Let the distance of the place be x km.
Speed downstream = (7.5 + 1.5) km/hr = 9 km/hr
Speed upstream = (7.5 - 1.5) km/hr = 6 km/hr

d 9

+

d 6

=

50 60

5d 18

=

5 6

d = 3 km