A can run 500 m in 30 seconds and B in 35 se | vedclass

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Question

(C) Time taken by $A$ to run $1 \ km$ $(1000 \ m)$ is $30 	imes 2 = 60 	ext{ seconds}$.Time taken by $B$ to run $1 \ km$ $(1000 \ m)$ is $35 	imes

Vedclass · Accepted Answer

$142 \frac{6}{7}$

Vedclass · Answer

(C) Time taken by $A$ to run $1 \ km$ $(1000 \ m)$ is $30 	imes 2 = 60 	ext{ seconds}$.Time taken by $B$ to run $1 \ km$ $(1000 \ m)$ is $35 	imes 2 = 70 	ext{ seconds}$.To end in a dead-heat,$A$ must give $B$ a head start equal to the distance $B$ covers in the time difference between $A$ and $B$.The time difference is $70 - 60 = 10 	ext{ seconds}$.Since $B$ runs $500 \ m$ in $35 	ext{ seconds}$,the speed of $B$ is $\frac{500}{35} 	ext{ m/s}$.Distance covered by $B$ in $10 	ext{ seconds} = \frac{500}{35} 	imes 10 = \frac{5000}{35} = \frac{1000}{7} = 142 \frac{6}{7} 	ext{ meters}$.Thus,$A$ can give $B$ a start of $142 \frac{6}{7} 	ext{ meters}$.

$A$ can run $500 \ m$ in $30$ seconds and $B$ in $35$ seconds. How many meters start can $A$ give to $B$ in a $1 \ km$ race so that the race may end in a dead-heat?

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