A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. what is the time taken by boat in still water?

Correct Answer: 9 km/hr, 3 km/hr

Explanation:

Let's call the speed of the boat in still water "b" and the speed of the river flow "r".
When the man goes downstream, he travels with the current, so his effective speed is b + r. When he goes upstream, he travels against the current, so his effective speed is b - r.
We know that the man traveled 28 km downstream and then immediately returned, so his total distance traveled is 56 km. We also know that it took him twice as long to make the return trip, so his time going upstream was twice his time going downstream.
Using the formula distance = rate x time, we can set up two equations:
28 = (b + r) * t1
28 = (b - r) * 2t1
where t1 is the time it took the man to go downstream.
Simplifying the second equation, we get:
14 = (b - r) * t1
Now let's consider what happens if the speed of the river flow is doubled. The new effective speed downstream would be b + 2r, and the new effective speed upstream would be b - 2r. The total distance traveled is still 56 km. We can set up two more equations:
56 = (b + 2r) * t2
56 = (b - 2r) * 2t2
where t2 is the new total time it takes to make the trip downstream and back.
Simplifying the second equation, we get:
28 = (b - 2r) * t2
Now we have four equations and four unknowns (b, r, t1, and t2). We can solve for them using substitution and elimination.
From the first equation, we can solve for t1:
t1 = 28 / (b + r)
From the second equation, we can solve for t1 in terms of t2:
t1 = 14 / (b - r)
Setting these two expressions for t1 equal to each other and simplifying, we get:
(b + r) / (b - r) = 2
Solving for r in terms of b, we get:
r = b / 3
Now we can substitute this expression for r into any of the four equations to solve for the other variables. Let's use the first equation:
28 = (b + r) * t1
28 = (4b/3) * t1
t1 = 21 / (2b)
Now we can use this expression for t1 to solve for t2 in terms of b:
t2 = 42 / (2b - 4r)
t2 = 42 / (2b - 4b/3)
t2 = 126 / b
Finally, we can use the third equation to solve for b:
56 = (b + 2r) * t2
56 = (4b/3 + 2b/3) * 126 / b
56 = 2 * 126
b = 9
So the speed of the boat in still water is 9 km/h, and the speed of the river flow is b/3 = 3 km/h.

Correct Answer: 180 km

Explanation:

Speed in downstream = (14 + 4) km/hr = 18 km/hr;

Speed in upstream = (14 ? 4) km/hr = 10 km/hr.

Let the distance between A and B be x km. Then,

x/18 + (x/2)/10 = 19 ? x/18 + x/20 = 19 ? x = 180 km.

Correct Answer: 4 2⁄3 Kmph

Explanation:

Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr Given: Speed in still water = 9 (1/3) = 28/3 km/hr i.e, ½ (a+b) = 28/3 km/hr ½ (x+3x) = 28/3 2x = 28/3 x = 28/ 2 x 3 = 14/3 km/hr rate upstream b = 14/3 km/hr and rate downstream a = 14/3 x 3 = 14 km/hr speed of the current = ½ (a-b) = ½ (14 – 14/3) = ½ (42-14/3) = 28/6 = 4 (2/3) km/hr

Correct Answer: 3h

Explanation:

Upstream speed = B-S

Downstream speed = B+s

B-S = 15/5 = 3 km/h

Again          B= 4S

Therefore    B-S = 3= 3S

=>             S = 1 and B= 4 km/h

Therefore    B+S = 5km/h

Therefore, Time during downstream = 15/5 = 3h

Correct Answer: Rs. 200

Explanation:

F = B D × T D B D - T D = 200 × 100 200 - 100 = 200 × 100 100 = R s . 200

Correct Answer: 6 kmph

Explanation:

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph

Correct Answer: 1.5 kmph

Explanation:

Speed of Boy is B = 4.5 kmph

Let the speed of the stream is S = x kmph

Then speed in Down Stream = 4.5 + x

speed in Up Stream = 4.5 - x

As the distance is same,

=> 4.5 + x = (4.5 - x)2

=> 4.5 + x = 9 -2x

3x = 4.5

x = 1.5 kmph

Correct Answer: 21 km

Explanation:

Let the distance covered be D km. 

  D 10 + 4 + D 10 - 4 = 5

  D 14 + D 6 = 5

 10D = 42 x 5 = 210

 

=> D = 21 km

Correct Answer: 5 kmph

Explanation:

Speed of the boat downstream  s=a/t= 60/3 = 20 kmph

Speed of the boat upstream s= d/t = 30/3= 10 kmph

 

Therefore,  The speed of the stream =  s p e e d o f d o w n s t r e a m - s p e e d o f u p s t r e a m 2=5 kmph

Correct Answer: 1/2 kmph

Explanation:

Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.

Speed in downstream = 3 x 60/18 = 10 km/hr

Rate of current = (10-9)/2 = 1/2 km/hr.