d The speed of a motor-boat solving word problem

# MCQ Word Problem 2 ( Boat in a stream and distance calculation )

MCQ Word Problem 2: The speed of a motor-boat is that of the current of water as 36:5. The boat goes along with the current in 5 hours 10 minutes. It will come back in:

A. 5 hours 50 minutes                 B. 6 hours              C. 6 hours 50 minutes           D. 12 hours 10 minutes

Solution:

For solving word problem we see;

We are given that ratio of speeds of boat and water current is;

36 : 5

i-e Speed of boat = 36

and Speed of current of water = 5

As the time is given in hours, so we assume speeds in km per hours i-e let us suppose;

Speed of Water = 36 km/h

Speed of water current = 5 km/h

If the boat is going downstream i-e in the direction of flow of water then, net speed of the boat will be sum of boat’s speed itself and the speed of water current. i-e suppose;

V=Net speed of boat downstream = 36+5=41 km/h

T= Time taken by the boat while going downstream= 5 hours +10 minutes = 5hours+ 10/60hours = 31/6 hours

S= Distance = ?

(To convert minutes into hours we divide minutes by 60 – because;

60 minutes = 1 hour

==> 1 minute = 1/60 hours

Inabove case, ==> 10 minutes = 10/60 hours)

We know S= VxT

put values of V and T there,

so,

$S= 41\times \frac{31}{6}=211.8 km$

## In how much time it will come back ?

The boat will have to move upstream to come back and in this case net  speed of the boat = Speed of boat – Speed of Water flow = 36-5 =31 km /h

Now we have calculated distance to be 211.8 km

We  need to calculate the time in which it will travel this distance upstream !

i-e

v= Speed of boat upstream = 31 km/h

s= Distance to be coverd upstream= 211.8 km

t= Time to  cover the distance = ?

Again we know;

$t=\frac{s}{v}$

Put values of s and v;

$t= \frac{211.8}{31}=6.83333333h$

i-e the boat will come back 6.833333333 hours = 6hours +0.833333333 hours

We convert 0.833333333 hours  into minutes by multiplying it with 60 – because there are 60 minutes in an hour.

so 0.833333333 hours = 0.833333333 x 60 = 49.9 = 50 minutes

So, the boat will come back in =6 hours + 50 minutes

Option c is correct here !