A and B run a kilometer and A wins by 25 , s. | vedclass

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Question

(A) Let $T_A, T_B, T_C$ be the time taken by $A, B,$ and $C$ to run $1000 \, m$ respectively.From the first condition,$T_B = T_A + 25$.From the third

Vedclass · Accepted Answer

$2 \, min \, 25 \, s$

Vedclass · Answer

(A) Let $T_A, T_B, T_C$ be the time taken by $A, B,$ and $C$ to run $1000 \, m$ respectively.From the first condition,$T_B = T_A + 25$.From the third condition,$B$ beats $C$ by $30 \, s$,so $T_C = T_B + 30 = (T_A + 25) + 30 = T_A + 55$.In the race between $A$ and $C$,$A$ covers $1000 \, m$ while $C$ covers $1000 - 275 = 725 \, m$.Since $A$ finishes the race,$T_A$ is the time taken by $A$. In this time,$C$ covers $725 \, m$.We know $T_C = T_A + 55$,which means $C$ takes $55 \, s$ more than $A$ to cover the remaining $275 \, m$.Speed of $C = \frac{275 \, m}{55 \, s} = 5 \, m/s$.Time taken by $C$ to run $1000 \, m$ is $T_C = \frac{1000 \, m}{5 \, m/s} = 200 \, s$.Since $T_C = T_A + 55$,we have $200 = T_A + 55$,so $T_A = 145 \, s$.$145 \, s = 2 \, min \, 25 \, s$.

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

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