# Difficult Time, Speed & Distance Solved QuestionAptitude Discussion

 Q. Two friends $A$ and $B$ run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. $A$ who runs faster laps $B$ in the middle of the $5^{th}$ round. If $A$ and $B$ were to run a 3 km race long race, how much start, in terms of distance, should $A$ give $B$ so that they finish the race in a dead heat?
 ✖ A. 545.45 metres ✔ B. 666.67 metres ✖ C. 857.14 metres ✖ D. Cannot be determined

Solution:
Option(B) is correct

$A$ and $B$ run around a circular track. $A$ laps $B$ in the middle of the $5^{th}$ lap. i.e. when $A$ has run four and a half laps he has covered a distance which is 1 lap greater than that covered by $B$'s.

Therefore, when $A$ runs  $\dfrac{9}{2}$ laps, $B$ runs $\dfrac{7}{2}$ laps

This is same as saying when $A$ runs 9 laps, $B$ runs 7 laps.

i.e in a race that is 9 laps long, $A$ can give $B$ a start of 2 laps.

So, if the race is of 3000 metres long, then $A$ can give $B$ a start of

$\left(\dfrac{2}{9}\right)\times 3000=$666.67 metres.

The information with regard to the length of the circular track is redundant information.