Answer

Verified

347.1k+ views

**Hint:**First of all, let the speed of stream be x. Now, the speed of the boat travelling upstream will be $15 - x$ and the speed of the boat travelling downstream will be $15 + x$. Now, as the time taken by boat travelling downstream and travelling upstream is 4 hr 30 minutes, form an equation and use the formula $Time = \dfrac{{dis\tan ce}}{{speed}}$.

**Complete step-by-step solution:**

In this question, we are given that the speed of the boat in still water is 15 km/hr and it travels 30 km downstream and then returns back to the starting point. The total time taken for this journey is 4 hours 30 minutes. Now, we need to find out the speed of the stream.

Now, let the speed of the stream be x.

Now, while travelling downstream, the speed of the boat will get a boost due to the speed of the stream flowing downwards too. Therefore,

$ \Rightarrow $Speed of boat travelling downstream $ = $ Speed of boat in still water + Speed of stream

$ \Rightarrow $ Speed of boat travelling downstream $ = 15 + x$

So, while travelling upstream, the speed of the boat will reduce due to the speed of the stream. Therefore,

$ \Rightarrow $Speed of boat travelling upstream $ = $ Speed of boat in still water – Speed of stream

$ \Rightarrow $ Speed of boat travelling upstream $ = 15 - x$

Now, the boat travels a distance of 30kms downstream, so it will travel a distance of 30kms only while travelling upstream. Therefore,

$ \Rightarrow $Downstream Distance$ = 30km$

$ \Rightarrow $Upstream Distance$ = 30km$

Now, it is given that the time taken by boat to travel 30kms downstream and then again 30kms upstream is 4 hours 30 minutes. Therefore,

$ \Rightarrow $Time taken to travel downstream + Time taken to travel downstream $ = $4 hour 30 minutes

Now, convert 4 hours 30 minutes into hours first.

$ \Rightarrow $4 hours 30 minutes $ = $ 4.5hr

Now, we know that

$

\Rightarrow Speed = \dfrac{\text{distance}}{\text{time}} \\

\Rightarrow Time = \dfrac{\text{distance}}{\text{speed}} $

Therefore, using this formula, we get

$

\Rightarrow \dfrac{\text{Downstream- distance}}{\text{Downstream- speed}} + \dfrac{\text{Upstream - distance}}{\text{Upstream - speed}} = 4.5 \\

\Rightarrow \dfrac{{30}}{{15 + x}} + \dfrac{{30}}{{15 - x}} = 4.5 $

Taking 30 common and taking LCM on the LHS, we get

$

\Rightarrow 30\left( {\dfrac{1}{{15 + x}} + \dfrac{1}{{15 - x}}} \right) = 4.5 \\

\Rightarrow \dfrac{{15 - x + 15 + x}}{{\left( {15 + x} \right)\left( {15 - x} \right)}} = \dfrac{{4.5}}{{30}} \\

\Rightarrow \dfrac{{30}}{{225 - 15x + 15x - {x^2}}} = 0.15 $

Now, cross multiplying, we get

$

\Rightarrow \dfrac{{30}}{{0.15}} = 225 - 15x + 15x - {x^2} \\

\Rightarrow 200 = 225 - {x^2} $

Gathering all the like terms, we get

$

\Rightarrow {x^2} = 225 - 200 \\

\Rightarrow {x^2} = 25 \\

\Rightarrow x = \pm 5 $

**But, speed cannot be negative, so the speed of the stream will be \[x = 5km/hr\].**

**Note:**Note that here the most important is deciding the speeds of the boat while travelling upstream and downstream. When the boat travels upstream, the water is going to oppose the boat so the speed is always going to be less than that of still water. And when the boat is travelling downstream, the speed of the boat is always going to be more than the actual speed as it gets help from the stream that moves downward too.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE