Answer
Verified
467.1k+ views
Hint: In downstream, the boat goes with the water-flow so we add both the speeds of boat and water and in upstream, boat goes against the direction of water-flow so we subtract both the speeds. Then we use the formula for speed to find the answer.
Complete step-by-step answer:
Let the speed of the stream be x$\dfrac{{{\text{km}}}}{{{\text{hr}}}}$.
Then,
Speed downstream = (15 + x) $\dfrac{{{\text{km}}}}{{{\text{hr}}}}$
Since the still water is going downstream. The speeds add up.
Speed upstream = (15 - x) $\dfrac{{{\text{km}}}}{{{\text{hr}}}}$
Since the still water is going downstream. The speeds are subtracted.
Speed = $\dfrac{{{\text{total distance covered}}}}{{{\text{total time taken}}}}$
Total time = $\dfrac{{{\text{total distance covered}}}}{{{\text{speed}}}}$
Given distance d = 30km
Total time t = 4$\dfrac{1}{2}$hours
Total time = Time take to travel downstream + Time taken to travel upstream
⟹$\dfrac{{30}}{{{\text{15 + x}}}} + \dfrac{{30}}{{{\text{15 - x}}}} = 4\dfrac{1}{2}$
$
\Rightarrow \dfrac{{\left[ {30\left( {15 - {\text{x}}} \right) + 30\left( {{\text{15 + x}}} \right)} \right]}}{{\left( {{\text{15 + x}}} \right)\left( {{\text{15 - x}}} \right)}} = \dfrac{9}{2} \\
\Rightarrow \dfrac{{\left[ {450 - 30{\text{x + 450 + }}30{\text{x}}} \right]}}{{225 + 15{\text{x - 15x - }}{{\text{x}}^2}}} = \dfrac{9}{2} \\
$
$
\Rightarrow \dfrac{{900}}{{225 - {{\text{x}}^2}}} = \dfrac{9}{2} \\
\Rightarrow \dfrac{{100}}{{225 - {{\text{x}}^2}}} = \dfrac{1}{2} \\
\Rightarrow 200 = 225 - {\text{ }}{{\text{x}}^2} \\
\Rightarrow {{\text{x}}^2} = 25 \\
\Rightarrow {\text{x = 5}}\dfrac{{{\text{km}}}}{{{\text{hr}}}} \\
$
Hence, the speed of the stream is 5$\dfrac{{{\text{km}}}}{{{\text{hr}}}}$.
Note: In order to solve this type of questions the key is to identify that in downstream both the speeds are added up and when in upstream both the speeds are subtracted. Using the formula for speed is the next step we proceed with. Then we equate the total time and individual times taken to calculate the answer.
Complete step-by-step answer:
Let the speed of the stream be x$\dfrac{{{\text{km}}}}{{{\text{hr}}}}$.
Then,
Speed downstream = (15 + x) $\dfrac{{{\text{km}}}}{{{\text{hr}}}}$
Since the still water is going downstream. The speeds add up.
Speed upstream = (15 - x) $\dfrac{{{\text{km}}}}{{{\text{hr}}}}$
Since the still water is going downstream. The speeds are subtracted.
Speed = $\dfrac{{{\text{total distance covered}}}}{{{\text{total time taken}}}}$
Total time = $\dfrac{{{\text{total distance covered}}}}{{{\text{speed}}}}$
Given distance d = 30km
Total time t = 4$\dfrac{1}{2}$hours
Total time = Time take to travel downstream + Time taken to travel upstream
⟹$\dfrac{{30}}{{{\text{15 + x}}}} + \dfrac{{30}}{{{\text{15 - x}}}} = 4\dfrac{1}{2}$
$
\Rightarrow \dfrac{{\left[ {30\left( {15 - {\text{x}}} \right) + 30\left( {{\text{15 + x}}} \right)} \right]}}{{\left( {{\text{15 + x}}} \right)\left( {{\text{15 - x}}} \right)}} = \dfrac{9}{2} \\
\Rightarrow \dfrac{{\left[ {450 - 30{\text{x + 450 + }}30{\text{x}}} \right]}}{{225 + 15{\text{x - 15x - }}{{\text{x}}^2}}} = \dfrac{9}{2} \\
$
$
\Rightarrow \dfrac{{900}}{{225 - {{\text{x}}^2}}} = \dfrac{9}{2} \\
\Rightarrow \dfrac{{100}}{{225 - {{\text{x}}^2}}} = \dfrac{1}{2} \\
\Rightarrow 200 = 225 - {\text{ }}{{\text{x}}^2} \\
\Rightarrow {{\text{x}}^2} = 25 \\
\Rightarrow {\text{x = 5}}\dfrac{{{\text{km}}}}{{{\text{hr}}}} \\
$
Hence, the speed of the stream is 5$\dfrac{{{\text{km}}}}{{{\text{hr}}}}$.
Note: In order to solve this type of questions the key is to identify that in downstream both the speeds are added up and when in upstream both the speeds are subtracted. Using the formula for speed is the next step we proceed with. Then we equate the total time and individual times taken to calculate the answer.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
A group of fish is known as class 7 english CBSE
The highest dam in India is A Bhakra dam B Tehri dam class 10 social science CBSE
Write all prime numbers between 80 and 100 class 8 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Onam is the main festival of which state A Karnataka class 7 social science CBSE
Who administers the oath of office to the President class 10 social science CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Kolkata port is situated on the banks of river A Ganga class 9 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE