Question

A swimmer swims 90m long pool. He covers the distance of 180m by swimming from

one end to other end back along the same path. If he covers the first 90m at speed of 2m/s,

then how fast he swim so that his average speed is 3m/s?​

Answer 1

${\large{\pmb{\sf{\underline{Required \: solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{About \: question...}}}}}$

⋆ Correct question: A swimmer swims 90m long pool. He covers the distance of 180 m by swimming from one end to other end back along the same path. If he covers the first 90 m at speed of 2 m/s, then how fast he swim so that his average speed is 3 m/s?

⋆ Understanding the question: This question says that there is a swimmer, who swims in a pool which is 90 metres in length. Then he covers the distance of 180 metres by swimming from one end to other end back along the same path. Now this question says that we he covers the first 90 metres at speed of 2 m/s, then how fast he swim so that his average speed is 3m/s. Let us solve this question!

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

⋆ Length of pool = 90 metres

⋆ He covers the distance of 180 m by swimming from one end to other end back along the same path.

⋆ He covers the first 90 metres at speed of 2 metre per second.

⋆ His average speed is 3 m/s

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ As he covers the first 90m at speed of 2m/s, then how fast he swim so that his average speed is 3m/s?

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ He can swim fast at 6 second so that his average speed is 3m/s.

${\bigstar \:{\pmb{\sf{\underline{Using \: concepts...}}}}}$

⋆ Formula to find out time taken

⋆ Formula to find out average speed

⋆ Formula to find out the speed

${\bigstar \:{\pmb{\sf{\underline{Using \: formulas...}}}}}$

${\small{\underline{\boxed{\sf{\star Time \: taken \: = \dfrac{Distance}{Speed}}}}}}$

${\small{\underline{\boxed{\sf{\star Speed \: taken \: = \dfrac{Distance}{Time}}}}}}$

${\small{\underline{\boxed{\sf{\star Average \: Speed \: = \dfrac{Total \: Distance}{Total \: Time}}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ Firstly let us find the time as it is given that he covers the first 90 metres at speed of 2 metre per second.

$\dashrightarrow \rm Time \: taken \: = \dfrac{Distance}{Speed} \\ \\ \dashrightarrow \rm Time \: taken \: = \dfrac{90}{2} \\ \\ \dashrightarrow \rm Time \: taken \: = \cancel{\dfrac{90}{2}} \\ \\ \dashrightarrow \sf Time \: taken \: = 45 \: seconds$

~ Now (recalling) as it's given that he covers the first 90 metres at speed of 2 metre per second means he cover his next 90 metres at ${\rm{t_2}}$ It is also provided that he covers the distance of 180 m by swimming

$\dashrightarrow \rm Distance \: = 180 \: m \\ \\ \dashrightarrow \rm Time \: taken \: to \: cover \: 180 \: metres \: = 45 + t_2 \\ \\ \dashrightarrow \sf 180 = 45 + t_2$

~ Now it is given to us that the first 90 metres at speed of 2 metre per second and his average speed is 3 m/s Therefore,

$\dashrightarrow \rm Average \: Speed \: = \dfrac{Total \: Distance}{Total \: Time} \\ \\ \dashrightarrow \rm 3 \: = \dfrac{180}{45+t_2} \\ \\ \dashrightarrow \rm \dfrac{180}{3} = 45+t_2 \\ \\ \dashrightarrow \rm \cancel{\dfrac{180}{3}} = 45+t_2 \\ \\ \dashrightarrow \rm 60 = 45+t_2 \\ \\ \dashrightarrow \rm 60 - 45 = t_2 \\ \\ \dashrightarrow \rm 15 = t_2 \\ \\ \dashrightarrow \rm t_2 \: = 15 \: seconds \\ \\ \dashrightarrow \sf Time \: to \: came \: back \: = 15 \: seconds$

~ Now at last let us find that how fast he swim so that his average speed is 3m/s. Firstly we get,

• Distance as 90 metres
• Time taken as 15 seconds

Now using formula to find speed

$\dashrightarrow \rm Speed \: = \dfrac{Distance}{Time} \\ \\ \dashrightarrow \rm Speed \: = \dfrac{90}{15} \\ \\ \dashrightarrow \sf Speed \: = 6 \: metres$