Boat M can cover 14 km upstream and 21 km downstream together in 3 hours. Also it can cover 21 km upstream and 42 km downstream together in 5 hours. What is the speed of current?
Upstream speed in both cases is 14 and 21 resp. Ratio is 14 : 21 = 2 : 3. So let times in both cases be 2x and 3x
Downstream speed in both cases is 21 and 42 resp. Ratio is 21 : 42 = 1 : 2. So let times in both cases be y and 2y
So 2x + y = 3
and 3x + 2y = 5
Solve both, x = 1, y = 1
So upstream speed is = 14/2x = 7 km/hr
And downstream = 21/y = 21 km/hr
So speed of current is 1/2 * (21-7) =7
Four times the downstream speed is 8 more than 15 times the upstream speed. If difference between downstream and upstream speed is 24 km/hr, then what is the ratio of speed in still water to the speed of the current?
Let speed in still water = x km/hr, of current = y km/hr
4 (x+y) = 15(x-y) + 8
Solve, 11x – 19y + 8 = 0…….(1)
Also (x+y) – (x-y) = 24
So y = 12
Put in (1). x = 20
So x/y = 20/12 = 5/3
RAM can row a certain distance downstream in 3 hours and return the same distance in 9 hours. If the speed of current is 18 km/hr, find the speed of RAM in still water.
B = [tu + td] / [tu – td] * R
B = [9+3] / [9-3] * 18
B = 36 km/hr
RAKESH can row 4 Km against the stream in 20 minutes and return in 24 minutes. Find the speed of RAKESH in still water.
At its usual rowing rate, a boat H can travel 18 km downstream in 4 hours less than it takes to travel the same distance upstream. But if he the usual rowing rate for his 28-km round trip was 2/3rd, the downstream 14 km would then take 12 hours less than the upstream 14 km. What is the speed of the current?
Let speed of boat H = x km/hr, and of current = y km/hr
18/(x-y) = 18/(x+y) + 4
Gives x2 = 9y + y2……..(1)
Now when speed of boat is 2x/3
14/(2x/3 -y) = 14/(2x/3 +y) + 12
42/(2x-3y) = 42/(2x+3y) + 12
Gives 4x2 = 21y + 9y2…………(2)
From (1), put value of x2 in (2) and solve
Solving, x = 6, y = 3
A SHIP takes 5 hours for travelling downstream from point A to point B and coming back to point C at 3/4th of total distance between A and B from point B. If the velocity of the stream is 3 kmph and the speed of the SHIP in still water is 9 kmph, what is the distance between A and B?
Let total distance from A to B= d km, So CB = 3d/4 km
d/(9+3) + (3d/4)/(9-3) = 5
Solve, d = 24 km
RANJAN can row at a speed of 15 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 9 km/hr. Find his average speed for total journey.
When the distance is same, then average speed throughout journey would be:
Speed downstream * Speed upstream/speed in still water.
So here average speed = (15+9)*(15-9)/15 = 9.6 km/hr
RAHUL rows to a certain place and comes back, but by mistake he covers 1/3rd more distance while coming back. The total time for this journey is 10 hours. The ratio of speed of boat to that of stream is 2 : 1. If the difference between upstream and downstream speed is 12km/hr, then how much time will the man take to reach to starting point from his present position?
Speed of boat and stream – 2x and x respectively. So downstream speed = 2x+x = 3x, and upstream speed = 2x-x = x
Let total distance between points is d km
So RAHUL covered d km downstream, and while coming back i.e. upstream he covers d + 1/3 *d = 4d/3 km
Total time for this journey is 10 hrs. So
d/3x + (4d/3)/x = 10
Solve, d = 6x
Now also given, that (2x+x) – (2x-x) = 12
Solve, x = 6
So d = 36 km
So to come to original point, he will have to cover 1/3 * 36 = 12 km
And with speed 3x = 18 km/hr(downstream)
So time is 12/18 * 60 = 40 minutes
Boat M can cover 25 km upstream and 42 km downstream together in 7 hours. Also it can cover 30 km upstream and 63 km downstream together in 9 hours. What is the speed of the boat M in still water?
Upstream speed in both cases is 25 and 30 resp. Ratio is 25 : 30 = 5 : 6. So let times in both cases be 5x and 6x
Downstream speed in both cases is 42 and 63 resp. Ratio is 42 : 63 = 2 : 3. So let times in both cases be 2y and 3y
So 5x + 2y = 7
and 6x + 3y = 9
Solve both, x = 1, y = 1
So upstream speed is = 25/5x = 5 km/hr
And downstream = 42/2y = 21 km/hr
So speed of boat is 1/2 * (5+21)=13