Question

The school record for the $4\times 100$m relay race is 59 seconds. When an anchor-runner gets the baton, already $45\dfrac{3}{2}$​ seconds are up. At what speed must he run in order to equal the school record?

Answer 1

Hint: Type of question is based on speed, distance and time problem. As we know,$D=S\times T$, in which ‘D’ is distance, ‘S’ is speed and ‘T’ is time. Anchor-runner is the final position of the relay race i.e. last track, and according to our question it is the last track of 100 meter. So we had to find out the speed the runner should run to complete that race in the record time.

Complete step by step answer:
Moving ahead with the question we had a relay track covered in 4 parts of 100 meter each (understood through$4\times 100$). An anchor-runner is the final position of a relay race i.e. last track, and in our question it is the last track of 100 meter. According to given information in question;
Distance runner will run $=4\times 100=400m$
Record time of race$=59\sec $
Time taken to complete 3 round of relay race$=45\dfrac{3}{2}=\dfrac{93}{2}$
So remaining time for last track to complete in record time is equal to record time subtracted to time taken to complete three rounds i.e.
$\begin{align}
  & =59-\dfrac{93}{2} \\
 & =\dfrac{25}{2}\sec \\
\end{align}$
So in order to complete in the record time runner should complete the last round of the relay race in$\dfrac{25}{2}\sec $. As we know that distance runners had to travel to complete the last round is equal to 100m. So to know the speed at which runner should run to complete the last round in$\dfrac{25}{2}\sec $, we have a relation between speed, distance and time i.e. $D=S\times T$
So going with the relation to find out the speed for last track, we will get;
$\begin{align}
  & D=S\times T \\
 & 100m=S\times \dfrac{25}{2} \\
 & S=8{\scriptstyle{}^{m}/{}_{s}} \\
\end{align}$
Hence anchor runner should run at $8{\scriptstyle{}^{m}/{}_{s}}$ in order to complete the relay race in the record time.

Note: Keep in mind that when we take distance in meter, and time in second then speed will come in meter per second. As a unit is given preference, if you write the wrong unit then your answer will be counted as wrong.