d Speed of motor boat ...... boat in still water

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

## Speed of motor boat …… boat in still water

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 )