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Three athletes A, B and C run a race, B finished `24` meters ahead of C and `36` meters ahead of A, while C finished `16` meters ahead of A. If each athlete runs the entire distance at their respective constant speeds, what is the length of the race ? |
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Answer» Length of the race be `D_m`,`t_b` units `(V_b-V_c)t_b=24m-(1)` `(V_c-V_a)t_b=12m-(2)` `(V_c-V_a)(t_b+24/V_c)=16m-(3)` `D=V_bt_b` `V_bt_b-V_ct_b=24` `D-V_ct_b=24-(4)` `V_a/V_c=5/6` `(V_b-V_a)t_b=36` `V_bt_b-V_at_b=36-(5)` `D-24=V_ct_b-(6)` `D-36=V_at_b`-(7) `(D-24)/(D-26)=V_c/C_a=6/5` `(D-24)5=(D-36)6` D=96m. |
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