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MCQ Word Problem 3 ( Speed of motor boat downstream and upstream and distance given, to find speed of stream )

 MCQ Word Problem 3: The speed of a boat in still water is 5 km/hr, it can go 30km upstream and return downstream to the original point in 4 hours 30 min. The speed of the stream is_______?

a) 5km/hr               b) 8 km/hr                        c) 10 km/hr                       d) 15 km/hr

Solution:

 

Here we suppose that ‘x’ be the speed of the stream water.

Because it is given that speed of motor boat in still water (i-e negligible flow) is 5 km/h, so its speed downstream is;

Speed of boat downstream= (x+5) km/h

and

Speed of the boat upstream = (5-x) km/h

As we know ;

\[ Distance = Speed \times Time \]

or

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

So,

Time for going downstream 30 kms ​\( = \frac{30}{5+x} \)

Time for coming upstream 30 kms ​\( = \frac{30}{5-x} \)

For this we can say,

Total time for going and coming back = ​\( = \frac {30}{5+x} + \frac{30}{5-x} \)

But total time for going and coming back (as given) = 4 hours + 30 minutes = 4 hours+0.5 hours = 4.5 hours !

So,

\[ \frac {30}{5+x} + \frac{30}{5-x} =4.5 \]

or

\[ \frac{300}{25-x^2}=4.5 \]

\[ 300= 4.5 \times 25-4.5x^2 \]

or

\[ 300=25-4.5x^2 \]

or

\[ 275=4.5x^2 \]

or

\[ x^2= \frac{275}{4.5}=61.11111 \]

or

\[ x= 7.8 km /h \]

Or

we can say that speed of stream flow  is  8 km  per hour – option b is correct !

 

Note: (Some sources have reported this problem with ‘speed of boat as 15 km/hr

hence, in such a case answer will be option a )

 

 

 

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