Boat-Stream

11 )

A man can row 40 kmph in still water and the river is running at 10 kmph. If the man takes 2 hr to row to a place and back, how far is the place?

38km

37.5km

40.75km

41km

None of these

View Solution

Answer :

Given

u=40 , v=10 D= t[(u²-v²)/2u] =2*[(40²-10²)/2* 40] =2*(1600-100)/80 2*1500/80==>37.5km

12 )

A man rows to a place 60 km distant and come back in 35 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the speed in still water and in stream:

1.5, 2

0.5, 2.5

3.5, 0.5

2, 2.5

None of these

View Solution

Answer :

If he moves 4 km downstream in x hours.

Downstream speed=4/x

Upstream speed=3/x

Then 60/(4/x) + 60/(3/x)=35

60[(3x+4x)/12]=35

60*7x/12=35

5*7x=35==> x=1km.

Then Downstream speed=4km/hr ,

Upstream speed=3km/hr

U=(4+3)/2=7/2=3.5km/hr

V=(4-3)/2=1/2=0.5km/hr

13 )

Speed of a boat in standing water is 12 kmph and the speed of the stream is 3 kmph. A man rows to a place at a distance of 6300 km and comes back to the starting point. The total time taken by him is:

1120hrs

1000hrs

980hrs

850hrs

None of these

View Solution

Answer :

Downstream speed = (12 + 3) = 15 km/hr

Upstream speed = (12 - 3) = 9 km/hr

Total time taken =6300/15+6300/9 =420+700==>1120hrs.

14 )

A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?

210km

185km

140km

168km

None of these

View Solution

Answer :

Downstream speed = 10+4 = 14

Upstream speed = 10-4 = 6

Now total time is 26 hours

If distance between A and B is d, then

distance BC = d/2

Now distance/speed = time, so

d/14 + (d/2)/6= 26

13d/84=26

Solve, d = 168 km ⁵

15 )

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

2 2/3mph

2mph

1 1/4mph

3mph

None of these

View Solution

Answer :

Let the speed of Rahul in still water be x mph

and the speed of the current be y mph

Then, Speed upstream = (x - y) mph

Speed downstream = (x + y) mph

Distance = 12 miles

Time taken to travel upstream - Time taken to travel downstream = 6 hours 12/(x-y) - 12/(x+y)=6

x²=y²+4y—1

Now he doubles his speed. i.e., his new speed = 2x

Now,

Speed upstream = (2x - y) mph

Speed downstream = (2x + y) mph

In this case, Time taken to travel upstream - Time taken to travel downstream = 1 hour

12/(2x-y) - 12/(2x+y) = 1 4x²=y²+24y—2

From 1 and 2 we get 4y+y²=(24y +y²)/4 Y=8/3==> 2 2/3mph

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