# Boats-streams practice test

1.

Speed of a boat in standing 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:

Explanation:

Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.

Total time taken =105/7.5  +105/10.5 hours = 24 hours.

2.

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

3.

A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. the speed of the stream (in km/hr) is:

Explanation:

Let the speed of the stream be x km/hr.
Then, Speed downstream = (15+x) km/hr,
Speed upstream = (15-x)km/hr
:. 30/(15+x) + 30/(15-x) = 4 ½
900/(225 –x2 = 9/2
9×2 = 225
x2 = 25
x = 5 km/hr

4.

In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

Explanation:

Speed in still water = 1/2= (11 + 5) kmph = 8 kmph.

5.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

Explanation:

6.

If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40 km/hr, then what is the speed of the stream ?

Explanation:

Speed of stream = ½( down stream – up stream )

= ½ ( 40 – 14 ) = 13 km/hr.
7.

A ship leaves on a long voyage. When it is 18 miles from the shore, a seaplane, whose speed is 10 times that of the ship, is sent to deliver mail. How far from the shore, does the seaplane catch up with the ship?

Explanation:

(d-18) =st; d= 10 *st; d=10 * (d-18), 180= 9d; d=20

8.

A crew can row 10 miles in 5/6 th of an hour down-stream and 12 miles upstream in 90 minutes. Find the current’s rate and crew’s rate in still water.

Explanation:

Downstream speed = 12 m/hr.
Upstream speed = 8 m/hr.

Current’s speed = (12 – 8) / 2= 2 m/hr..
Crew’s speed in still water = (12+8)/2 = 10 m/hr
9.

A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.

Explanation:
Let the upstream speed be U and the downstream speed be D
Boat speed in still water be B and stream speed be S
Therefore, U = B-S – – – (1)
D = B+S – – -(2) (1)+(2) ⇒ B = (U+D)/2
(1)-(2) ⇒ S = (U~D)/2
Let x and y be the upstream and downstream speed respectively.
Time = Distance/speed ⇒ 50/x + 72/y = 9 and 70/x+90/y = 12
Solving for x and y we get x = 10 kmph and y = 18 kmph
We know that Speed of the stream = ½(downstream speed – upstream speed) = ½(18 – 10) = 4 kmph
10.

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

Explanation:

Let the speed of the stream x mph. Then,
Speed downstream = (10 + x) mph,Speed upstream = (10 – x) mph.

36/(10 – x)- 36/(10 + x)     = 90/60

72x * 60 = 90 (100 – x2)

x2 + 48x – 100 = 0

(x+ 50)(x – 2) = 0

x = 2 mph.