Q: A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river?

Let mans 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

Question 1

A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:

Accepted Answer

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

Question 2

A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river?

Accepted Answer

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

Question 3

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distanc…

Accepted Answer

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.

Question 4

A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed o…

Accepted Answer

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.

Question 5

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?

Accepted Answer

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by 2 × t 1 × t 2 t 1 + t 2 = 2 × 12 × 24 36 = 16 h

Question 6

The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?

Accepted Answer

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

Question 7

A boy can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is ?

Accepted Answer

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

Question 8

A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the strin…

Accepted Answer

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

Question 9

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?

Accepted Answer

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

Question 10

A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?

Accepted Answer

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.

Question 11

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?

Accepted Answer

Speed in still water = 6 kmph Stream speed = 1.2 kmph Down stream = 7.2 kmph Up Stream = 4.8 kmph x/7.2 + x/4.8 = 1 x = 2.88 Total Distance = 2.88 x 2 = 5.76 kms

Question 12

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?

Accepted Answer

Let the speed of the boat upstream be p kmph and that of downstream be q kmph Time for upstream = 8 hrs 48 min = 8 4 5 hrs Time for downstream = 4 hrs Distance in both the cases is same. => p x 8 4 5 = q x 4 => 44p/5 = 4q => q = 11p/5 Now, the required ratio of Speed of boat : Speed of water current = q + p 2 : q - p 2 => (11p/5 + p)/2 : (11p/5 - p)/2 => 8 : 3

Question 13

A boat whose speed in still water is 9 kmph, goes 12 km downstream and comes back in 3 hrs. Find the speed of the stream?

Accepted Answer

Let the speed of the stream = x kmph From the given data, 12 9 + x + 12 9 - x = 3 h r s 3 x 2 = 27 => x = 3 kmph Therefore, the speed of the stream = 3 kmph

Question 14

A man can row 8 kmh in still water. If the river is running at 2 kmh, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by

Accepted Answer

Let the distance be d. d 8 - 2 - d 8 + 2 = 4 => 2d = 120 => d = 60 kms.

Question 15

A motorboat can go 10 miles downstream on a river in 20 min. It takes 30 min for this boat to go back at the same 10 miles. Find the speed of the current ?

Accepted Answer

As the distance travelled is constant, the time taken is inversely proportional to speed. Let 'u' be the speed of the current and 'v' be the speed of the boat. Speed of the boat downstream = v + u & upstream = v - u => v+u/v-u = 30/20 => v/u = 5 => v = 5u => v + u = 6u = 10/20/60 miles/hr => 6u = 30 m/h => u = 5 m/h

Question 16

In one hour, a boat goes 12 km/hr along the stream and 6 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

Accepted Answer

Speed in still water = Average of Speed in Upstream and speed in Downstream = 1/2 (12 + 6) kmph = 9 kmph.

Question 17

If sum of upstream and downstream speed of a boat is 82 kmph, and the boat travels 105 km. upstream in 3 hr, Find the time taken by boat to cover 126 km downstream.

Accepted Answer

Let Speed of boat in still water = b Let Speed of still water = w Then we know that, Speed of Upstream = U = boat - water Speed of Downstream = D = boat + water Given, U + D = 82 b - w + b + w = 82 2b = 82 => b = 41 kmph From the given data, 41 - w = 105/3 = 35 w = 6 kmph Now, b + w = 126/t => 41 + 6 = 126/t => t = 126/47 = 2.68 hrs.

Question 18

A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?

Accepted Answer

Downstream speed = 72km/8hrs = 9 kmph upstream speed = 84km/12hrs = 7 kmph speed of boat = avg of downstream and upstream speeds speed of boat = (9+7)/2kmph = 8 kmph. current speed = half of the difference of downstream and upstream speeds currend speed = (9-7)/2kmph = 1 kmph

Question 19

A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?

Accepted Answer

Speed in downstream = 96/8 = 12 kmph Speed of current = 4 km/hr Speed of the boatman in still water = 12 – 4 = 8 kmph Speed in upstream = 8 – 4 = 4 kmph Time taken to cover 8 km upstream = 8/4 = 2 hours.

Question 20

Rajesh rows in still water with a speed of 4.5 kmph to go to a certain place and comes back. Find his average speed for the whole journey, if the river is flowing with a speed of 1.5 kmph?

Accepted Answer

Let the distance in one direction = k kms Speed in still water = 4.5 kmph Speed of river = 1.5 Hence, speed in upstream = 4.5 - 1.5 = 3 kmph Speed in downstream = 4.5 + 1.5 = 6 kmph Time taken by Rajesh to row upwards = k/3 hrs Time taken by Rajesh to row downwards = k/6 hrs Now, required Average speed = Total distance Total speed = 2 k k 3 + k 6 = 2 k x 18 6 k + 3 k = 4 kmph Therefore, the average speed of the whole journey = 4kmph.

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