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MCQ Word Problem 1 ( Boat in a stream and distance calculation )

MCQ Word Problem 1: A steamer goes downstream from one port to another in 4 hours, it covers the same distance upstream in 5 hours. If the speed of the stream is 2km/hr,the distance between the two parts is______?

a) 50 km/hr                    b) 60 km/hr                       c) 70 km/hr                        d) 80 km/hr

Solution:

We know ;

Distance = Speed x Time

So,

\[ Speed = \frac{Distance}{Time} \]

Let Distance between two ports is ‘x’

Upstream

Speed of Streamer = ​\( \frac{x }{5}\frac{Km}{hr} \)

Downstream

Speed of Streamer = ​\( \frac{x }{4}\frac{Km}{hr} \)

We know that ;

Speed of Stream  = ​\( \frac{His Downstream Speed – His Upstream Speed}{2} \)

So,

Speed of Stream =​\( \frac{x/4-x/5}{2}\frac{km}{hr} \)

But given that speed of stream is 2 km/hr;

So,

\[ 2=\frac{x/4-x/5}{2}\frac{km}{hr} \]

Simplifying we get;

\[ x=80 \]

So the distance between two ports is 80 kms – option d is correct!

 


 

 

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