A and B run a kilometer and A wins by 25 text | vedclass

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Question

(A) Let $T_A, T_B, T_C$ be the time taken by $A, B, C$ to run $1000 	ext{ m}$.From the problem: $T_B - T_A = 25 	ext{ sec} \implies T_B = T_A + 25$.

Vedclass · Accepted Answer

$2 	ext{ min } 25 	ext{ sec}$

Vedclass · Answer

(A) Let $T_A, T_B, T_C$ be the time taken by $A, B, C$ to run $1000 	ext{ m}$.From the problem: $T_B - T_A = 25 	ext{ sec} \implies T_B = T_A + 25$.$A$ beats $C$ by $275 	ext{ m}$,meaning in time $T_A$,$C$ covers $1000 - 275 = 725 	ext{ m}$.Speed of $C = \frac{725}{T_A}$.Time taken by $C$ to run $1000 	ext{ m}$ is $T_C = \frac{1000}{725/T_A} = \frac{1000}{725} T_A = \frac{40}{29} T_A$.Given $T_C - T_B = 30 	ext{ sec}$.Substituting values: $\frac{40}{29} T_A - (T_A + 25) = 30$.$\frac{11}{29} T_A = 55 \implies T_A = 55 	imes \frac{29}{11} = 5 	imes 29 = 145 	ext{ sec}$.Wait,re-evaluating: The problem states $B$ wins by $30 	ext{ sec}$ over $C$. $T_C - T_B = 30$.Using $T_A = 145 	ext{ sec}$,$T_B = 170 	ext{ sec}$,$T_C = 200 	ext{ sec}$.$T_A = 145 	ext{ sec} = 2 	ext{ min } 25 	ext{ sec}$.

$A$ and $B$ run a kilometer and $A$ wins by $25 \text{ sec}$. $A$ and $C$ run a kilometer and $A$ wins by $275 \text{ m}$. When $B$ and $C$ run the same distance,$B$ wins by $30 \text{ sec}$. The time taken by $A$ to run a kilometer is

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