Question

A runs 100 metres in 11 seconds and B runs 100 meters in 12 seconds. The start which must be given to B to
make the race to be completed in 11 seconds with a draw will be.

Answer 1

Hint: First calculate the speed of A and B using the formula of speed and then calculate the distance covered by A and B in 11 seconds.

Formula used: Remember the triangle of distance, speed and time. If you wish to calculate speed, then put your thumb over ‘s’, $\dfrac{d}{t},$ remains which becomes the formula for speed. Similarly for distance and time.

Complete step-by-step answer:

Distance covered by A = 100 m
Time taken by A = 11 seconds
Speed of A , S A = $\dfrac{{distance}}{{time}}$
Put the value of distance and time in this formula.
$ = \dfrac{{100}}{{11}}m/s$
Distance covered by B = 100m
Time taken by B = 12 seconds
Put the value of distance and time in this formula.
Speed of B, S B = \[\dfrac{{distance}}{{time}}\]
\[ = \dfrac{{100}}{{12}}m/s\]
Now, to make the race draw, means both must complete the race in the same time in 11 seconds.
Distance covered by A in 11 seconds = speed of A(S A ) time
Put the value of speed and time in this formula.
=$\dfrac{{100}}{{11}} \times 11$
$ = 100m$
Distance covered by B in 11 seconds
= speed of B(S B ) time
=$\dfrac{{100}}{{12}} \times 11m$
$ = \dfrac{{1100}}{{12}}m$
$ = 91\dfrac{8}{{12}}$m
$ = 91\dfrac{2}{3}m$
$\therefore \,\,the\,\,start\,\,of B=\left( {100 - \dfrac{{1100}}{{12}}m} \right)$
\[ = \dfrac{{1200{\text{ - }}1100}}{{12}}\]m
$ = \dfrac{{100}}{{12}}m$
$ = 8\dfrac{4}{{12}}$m
$ = 8\dfrac{1}{3}m$must be given to B to make the race to be completed in 11 seconds.
Hence, a start of $8\dfrac{1}{3}m$must be given to B to make the race to be completed in 11 seconds.

Note: When solving these types of problems, make sure to write the appropriate units of speed and time in the final answer.Also, after you find out the distance of A and B , make sure to find out the difference between those two which will give the final answer.