Consider two cities `P` and `Q` berween which consistent bus servece is available in both directions. Every `x` mimutes `A` morning jogging towards `Q` from `P` wigh a speed of `10 km h^(-1)`. Every `18 mim` a bus crosses this jogger in its own direction of motion and every `6 min` another bus crosses in opposite derection. What is time prerilod between two consecutive buses and also find the speed of buses ?.

Explanation

The equations of motion are applicable in any frome of refernce. Attaching the frome of reference at jogger, the velocity of bus is now required w.r.t. jogger. Suppose speed of buses `=v km h^(1)`
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Distance between two buses on road: `s=xv`. The relative velocity of bus w.r.t. the hogger, for the buses moving from `P` to `Q`
`=(v-10) km h^(1)`. So we have
`18=(vx)/(v-10) rArr vx=18v -180` (i)
similarly. for the buses moving from `P` to `Q` relative veocity`=(v+10) km h^(-1)`. So we have
`6=(vx)/(v+10) rArr vx=6+60`........... (ii)
Solving (i) and (ii) we find `v=20 km h^(-1)` and `x=9 min`.