Boats and Streams with Explanation

Q8. If the speed of a boat is 15 km/hr and the ratio of downstream speed and upstream speed is 7 : 3. Find the speed of the stream?

Answer- Option A

Explanation-

Let the speed of the stream be x km/hr.
Speed downstream = (15 + x) km/hr
Speed upstream = (15 - x) km/hr

(15 + x) (15 - x)

=

7 3

45 + 3x = 105 - 7x
x = 6 km/hr

Q9. A motorboat rows 32 km downstream and 14 km upstream. If 6 hours is taken to cover each distance, then the velocity of the current is

Answer- Option B

Explanation-

Rate downstream

=

32 6

kmph

Rate upstream

=

14 6

kmph

Velocity of current =

32 6

-

14 6

kmph

=

3 2

kmph

=

1.5 kmph

Q10. A boatman takes twice as long to go a distance upstream as to travel the same distance downstream. What is the ratio of the speed of the boatman (in still water) and the current?

Answer- Option C

Explanation-

Let the speed of the boatman in still water be x km/hr and current be y km/hr.
Also, let the distance be d km
Speed downstream = (x + y) km/hr
Speed upstream = (x - y) km/hr

2

d (x + y)

=

d (x - y)

2(x - y) = x + y
x = 3y

x y

=

3 1

Q11. A pirate travels 15 km downstream of a river in 3 hours 45 minutes and 2 hours 30 minutes to row a boat 5 km upstream. What is the speed of the current?

Answer- Option C

Explanation-

Downstream speed =

15

x

4 15

=

4 km/hr

Upstream speed =

5

x

2 5

=

2 km/hr

Speed of current =

1 2

(4 - 2)

=

1 km/hr

Q12. A river is running at 2 km/hr, a boat goes 6 km downstream and comes back to the initial point in 33 minutes. Find the speed of the boat in still water?

Answer- Option A

Explanation-

Let the speed of the boat in still water be x km/hr.
Speed downstream = (x + 2) km/hr
Speed upstream = (x - 2) km/hr

6 (x + 2)

+

6 (x - 2)

=

33 60

11x² - 240x - 44 = 0
11x² - 242x + 2x - 44 = 0
(x - 22)(11x + 2) = 0
x = 22
Hence, speed of the boat in still water = 22 km/hr

Q13. A speedboat travels downstream from point P to point Q and comes back to a point R in 19 hours. Point R is a midway between point P and point Q. If the speed of the speedboat is 14 km/hr and velocity of the stream is 4 km/hr, what is the distance between point P and point Q?

Answer- Option D

Explanation-

Speed downstream = (14 + 4)km/hr = 18 km/hr
Speed upstream = (14 - 4)km/hr = 10km/hr
Let the distance between P and Q be x km.

x 18

+

(x/2) 10

=

19

x 18

+

x 20

=

19

x = 180 km

Q14. In still water, a boat can travel at 5 km/hr. It takes 1 hour to row to a place and come back. If the velocity of the stream is 1 km/hr, how far is the place?

Answer- Option B

Explanation-

Let the required distance be x km.
Speed downstream = (5 + 1)kmph = 6 kmph
Speed upstream = (5 - 1)kmph = 4 kmph
Then,

x 6

+

x 4

=

1

5x = 12
x = 2.4
The required distance is 2.4 km