Race running

**joyiu** · Oct 3rd 2011, 06:30 AM

Sneha,Shilpa,Sushma join a running race.The distance is 1500 metres.
Sneha beats Shilpa by 30 metres and Sushma by 100 metres.By how much
could Shilpa beat Sushma over the full distance if they both ran as
before?

**Soroban** · Oct 3rd 2011, 12:02 PM

Hello, joyiu!

This can be solved without Alger=bra ... just some serious Thinking.

$A,B, C$ have a 1500-meter race.

$A$ beats $B$ by 30 meters and $C$ by 100 meters.

By how much would $B$ beat $C$ over the full distance
. . if they both ran as before?

When $A$ ran 1500 meters:
. . $B$ ran only 1470 meters,
. . and $C$ ran a mere 1400 meters.

Hence, $C\ \!'\!s$ speed is only $\frac{1400}{1470} \,=\,\frac{20}{21}$ of $B\ \!'\!s$ speed.

When $B$ runs 1500 meters,
. . $B$ runs only: . $\frac{20}{21}\times 1500 \,\approx\,1428.6$ meters.

Therefore, $B$ beats $C$ by about: $1500 - 1428.6 \:=\:71.4$ meters.

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