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 ?
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.