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MCQ Word Problem 4 ( Boat, speed )

MCQ Word Problem 4 : A boat covers a distance of 30 km in 2 ½ hours running downstream while returning it covers the same distance in 3 ¾ hours. What is the speed of the boat in still water?

a) 8km/hr          b) 12km/hr             c) 14 km/hr           d) 15 km/hr     ) None of these

Solution:

 

Here we will apply formula of ‘swimmer’ given here !

i-e we will simply find out the average speed of the boat (taken as swimmer) – considering stream as still or having no flow of water.

We know;

Speed of swimmer  = 1/2(Ds+Us) {i-e his average speed)

 

Where,

Ds = speed of swimmer or boat downstream

Us = Speed of swimmer or boat upstream

To apply this formula we will have to calculate Ds and Us first !

Ds – Downstream speed

Distance = S= 30 km

Time  = t= 2.5 hrs

Speed =v= Ds = ?

We know;

Distance= Speed x Time

or

\[ S=vt \]

or

\[ v=\frac{S}{t} \]

Putting

v=Ds, S=30 km and t =2.5 hr

we get;

\[ Ds=\frac{30}{2.5}=12 km/hr \]

Us – Upstream speed

We have data for upstream

Distance=s= 30 km

Time =t= 3.75 hrs

Speed =v=Us=?

Using again above formula formula  and putting

v=Us, S=30 km and t =3.75 hr

we get;

\[ Us=\frac{30}{3.75}=8 km/hr \]

 

So the speed of the boat using formula

Speed of swimmer(the boat in our case) = 1/2(Ds+Us) {i-e his average speed)

we get;

Speed of the boat ​\( =\frac{12+8}{2}=10 km /hr \)

 

So the speed of the boat is 10 km/hr – our choice of answer is ‘e’

 

 

 

 

 

 

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