Stream Boat Problems

Upstream

Upstream questions are a subsection of the boat-stream or the boat-driver problems. Questions on the relative speed of the river or the stream with respect to the boat and the speed of the boat with respect to the river bank are present in this section. There are two main questions: on the downstream motion and on the upstream motion. In the following section, we will develop formulas and explain concepts that will help us solve these problems at a very fast pace. Let us begin!

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Upstream

The motion of the boat with respect to the river banks can be of two types. One of the types is when the boat goes in the same direction as the direction of the river. This is what we know as the downstream motion. However, when the boat goes in the opposite direction as that of the stream or the river, it is what we call the upstream motion. In the downstream motion, the boat and the water move in the same direction and thus the speed is more than what it will be when the two are moving opposite to each other. In other words, the upstream motion is slower.

Upstream

A man sitting in the boat will feel that the boat is moving but the water is still. This is the velocity of the boat with respect to water or the speed of the boat in still water. This speed is constant irrespective of the motion of the boat i.e. for both upstream and downstream motions. We denote this speed by ‘b’.

The speed of the river with respect to the banks of the river is what we call the rate of the flow of the stream. This is what we denote with the letter ‘r’. Therefore the speed upstream is (b – r) and the speed downstream is (b + r). Let us see a few solved examples and test these formulae.

Browse more Topics under Stream Boat Problems

Example 1: The speed of the boat is 10 km/h in still water. The speed of the current is 4 km/h, find out the distance that the boat covers in one hour when going upstream?

A) 6 km                B) 8 km                     C) 10 km                      D) 12 km

Answer: The speed of the boat in still water or ‘b’ = 10 km/h.

The speed of the current or the river = 4 km/h.

Therefore the speed of the boat when going upstream = b – r = 10 – 4 = 6 km/hr.

Therefore the distance covered in one hour = 6/1 = 6 km. Hence the correct option is A) 6 km.

 

Solved Examples For You

Example 2: A boat can travel with a speed of 13km/hr in still water. If the speed of the stream is 4km/hr. Find the time taken by the boat to go 81 km upstream?

A) 12.4 hr                  B) 540 minutes              C) 9 minutes                      D) 91 minutes

Answer: The speed of the boat in still water or ‘b’ is = 13 km/hr. Also, we have the speed of the stream or ‘r’ = 4 km/hr. Here we have to find the time taken by the boat to cover an upstream journey of 68 km. From the basic formula for the speed we have, speed = Distance/Time or in other words we can say that Time = Distance/speed.

We have the Distance for the journey = 81 km. Now we have to find the speed of the boat upstream. The upstream speed is = b – r = 13 – 4 = 9 km /hr.

Therefore using this in the formula for speed, we have: Time = 81/9 = 9 hr = (9 × 60) minutes = 540 minutes. Hence the correct option is B) 540 minutes.

Example 3: A motorboat, has a speed of 15 km/hr in still water. The motorboat goes 30 km downstream and comes back in a total of 4hrs and 30mins. The speed of the current is:

A) 5 km/hr                    B) 10 km/hr                        C) 15 km/hr                      D) 25 meters/minute

Answer: The speed of the motorboat in still water or ‘b’ = 15 km/hr. Let the speed of the river flow or the current = ‘r’ km/hr. Now let t1 be the time taken for the downstream journey and t2 be the time it takes for the upstream journey. Then as per the given conditions, we have:

t1 + t2 = 4 (1/2) hours. From the formula, Time = Distance/speed we have:

t1  = 30 km/(b + r) and  t2  = 3o km/(b – r); where the letters have their usual meanings. Substituting this in the equation above, we have:

30 km/(b + r) + 3o km/(b – r) = 4(1/2) hours. Since b = 15 km/hr, we can write upon cross multiplication of the terms: [30(15 – r) + 30 (15 + r)]/(15)2 – r2

This upon simplification will yield: 900/(25 – r2) = 9/2

Which can be further simplified into 200 = 225 – r2

or r = 5 km/hr. This is the speed of the current or the river and the correct option is A) 5 km/hr.

Practice Questions

Q 1: A man goes downstream as well as upstream in a boat. He takes twice as long to row upstream as he takes to row the same distance downstream. The ratio of the speed of the boat in still water and the speed of the stream is:

A) 1:3               B) 3:1                    C) 4:1                      D) 1:4

Ans: A) 1:3

Q 2: The speed of a boat is 5km/hr in still water. A man rows to a certain distance upstream and back to the starting point in a river. The speed of the flow is 2km/hr. Find the average speed for the total journey?

A) 3.9 km/hr                   B) 5.3 km/hr                C) 4 km/hr                  D) 4.2 km/hr

Ans: D) 4.2 km/hr

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