# TSD – Boats and Streams

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Boats and Streams is one of the common and scoring topics in the Quantitative Aptitude section of the CAT examination. The questions from this topic are very simple and easily solvable. To solve the questions from Boats and Streams all you need to do is to apply the formulas directly in the question and solve the basic equations.

The problems on boats and streams are dependent on the basic equation of time, speed and distance: Speed x Time = Distance. If you’re in a hurry, watch our tutorial video on this topic:

The boat has a speed of its own, which is also called the speed of the boat in still water.

Another variable that is used in boats and streams problems is the speed of the stream.

The speed of the movement of the boat is dependent on whether the boat is moving:

• In still water, the speed of movement is given by = $latex{ S }_{ B }$
• While moving upstream (or against the flow of the water), the speed  of movement is given by = $latex{ S }_{ U }\quad =\quad { S }_{ B }-{ S }_{ S }$
• While moving downstream (or with the flow of the water), the speed of movement is given by = $latex{ S }_{ D }\quad =\quad { S }_{ B }+{ S }_{ S }$

### Following are some important Terminologies and Formulas in Boats and Streams:

u = Speed of boat in still water.

v = Speed of the stream.

• Upstream

The term “Upstream” is the condition when the boat is moving opposite to the direction of the stream.

Upstream Speed = (u-v) km/hr

• Downstream

The term “Downstream” is the condition when the boat is moving in the same direction of the stream.

Downstream Speed= (u+v) km/hr

• Still Water

The speed of stream is zero i.e., the water is stationary.

Speed in still water = ½ (Upstream speed + Downstream speed)

• Speed of Stream

This is the flow of water at a certain speed.

Speed of Stream = ½ (Downstream speed – Upstream speed)

• Covering same distance upstream and downstream

If speed of boat in still water and speed of stream are ‘u’ and ‘v’ respectively and it covers the same distance upstream and downstream in t1 and t2 hours respectively, then

Average Speed = $latex\frac { (u-v)\quad \times \quad (u+v) }{ u }$

Also, $latex \frac { u }{ v } =\frac { t1+t2 }{ t1-t2 }$

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Q.1 Zen and Paul start from two points ‘d’ distance apart on a river and travel towards each other. Zen goes upstream and Paul goes downstream. They take time $latex { t }_{ A }$ to meet. If in second case, Paul goes upstream and Zen goes downstream then they take $latex { t }_{ B }$ time to meet. Compare $latex { t }_{ A }$ with $latex { t }_{ B }$ .

Ans: In both the cases the distance between them would be the same and also their relative speed moving towards each other would also be the same, because while calculating the relative speed the speed of the stream would get canceled. Hence both ways the time taken will be same only, $latex { t }_{ A }={ t }_{ B }$.

Q.2 A boat goes 40 km upstream in 8 h and a distance of 49 km downstream in 7 h. The speed of the boat in still water is;

(a) 5 km/h

(b) 5.5 km/h

(c) 6 km/h

(d) 6.5 km/h

Q.3 The speed of the boat in still water is 12 km/h and the speed of the stream is 2 km/h. A distance of 8 km, going upstream, is covered in

(a) 1 h

(b) 1 h 15 min

(c) 1 h 12 min

(d) None of these

Q.4 In a stream, B lies in between A and C such that it is equidistant from both A and C. A boat can go from A to B and back in 6 h 30 minutes while it goes from A to C in 9 h. How long would it take to go from C to A?

(a) 3.75 km

(b) 4 h

(c) 4.25 h

(d) 4.5 h

Q.5 In a stream that is running at 2 km/h, a man goes 10 km upstream and comes back to starting point in 55 minutes. Find the speed of the man in still water?

(a) 20 km/h

(b) 22 km/h

(c) 24 km/h

(d) 28 km/h

Q.6 A boat goes 15 km upstream in 80 minutes. The speed of the stream is 5 km/h. The speed of the boat in still water is

(a) 16.25 km/h

(b) 16 km/h

(c) 15 km/h

(d) 17 km/h

Answers: 1-(equal), 2-(c), 3-(d), 4-(b), 5-(b), 6-(a).