Answer

Verified

412.8k+ views

**Hint:**Whenever the boat is traveling upstream the then equivalent speed of the boat will be calculated by taking the difference of the speed of the boat and speed of the stream and if it is the case of upstream then the equivalent speed of the boat will be the sum of the speed of boat and stream. The formula to calculate time is ${\text{Time}} = \dfrac{{{\text{Distance}}}}{{{\text{Speed}}}}$.

**Complete step by step answer:**

Let, the speed of the stream be x.

It is given that the speed of the boat in the still water is 10 mph.

When the boat is traveling in the upstream, then it has to travel against the stream, so the speed of the boat will be the difference of boat in still water and speed of the stream, i.e., $10 - x$.

Similarly, when the boat is traveling in the downstream, then it has to travel with the stream, so the speed of the boat will be the sum of the speed of the boat in still water and speed of the stream, i.e., $10 + x$.

As, ${\text{Time}} = \dfrac{{{\text{Distance}}}}{{{\text{Speed}}}}$.

So, the time taken for the boat to travel upstream will be equal to $\dfrac{{36}}{{10 - x}}$.

Similarly, the time taken for the boat to travel downstream will be equal to $\dfrac{{36}}{{10 + x}}$.

It is given the time taken by the boat to travel upstream is 90 minutes more than to travel downstream.

Now, convert 90 minutes in hours by dividing it by 60, as in one hour there are 60 minutes,

so $\dfrac{{90}}{{60}} = \dfrac{3}{2}$ hours.

As the difference between time traveled by boat during upstream and downstream is $\dfrac{3}{2}$ hours.

Therefore,

$\dfrac{{36}}{{10 - x}} - \dfrac{{36}}{{10 + x}} = \dfrac{3}{2}$, now find the value of x by solving this equation.

$

\dfrac{{36}}{{10 - x}} - \dfrac{{36}}{{10 + x}} = \dfrac{3}{2} \\

\dfrac{{36\left( {10 + x} \right) - 36\left( {10 - x} \right)}}{{\left( {10 - x} \right)\left( {10 + x} \right)}} = \dfrac{3}{2} \\

\dfrac{{360 + 36x - 360 + 36x}}{{{{10}^2} - {x^2}}} = \dfrac{3}{2} \\

\dfrac{{72x}}{{100 - {x^2}}} = \dfrac{3}{2} \\

144x = 300 - 3{x^2} \\

3{x^2} + 144x - 300 = 0 \\

{x^2} + 48x - 100 = 0 \\

$

Now , factorize the equation ${x^2} + 48x - 100 = 0$ and find the value of x.

$

{x^2} + 48x - 100 = 0 \\

{x^2} + 50x - 2x - 100 = 0 \\

x\left( {x + 50} \right) - 2\left( {x + 50} \right) = 0 \\

\left( {x - 2} \right)\left( {x + 50} \right) = 0 \\

x = - 50,2 \\

$

As the value x cannot be negative because if we substitute this value to calculate the time taken for the boat to travel downstream will be negative and time cannot be negative.

So, the speed of the stream is 2 mph.

Therefore, option (A) is the correct answer.

**Note:**

This is the case of stream and boat, let the speed of the stream be some value x and use the formula of time to equate both the time taken by the boat, as it is mentioned in the question that it takes 90 minutes of more time to travel upstream than downstream, using this and formula of time the speed of stream can be calculated.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

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

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail