Two cars A and B are separated by a distance of 4 km. Car A is travelling at 72 kmph and car B at 54 kmph. After what time car A meets car B if the two are (i) travelling in the same direction and (ii) travelling in opposite directions.

Explanation

Relative velocity `=72-54="18 kmph"`
`"time taken by A to cross B"=("4 km")/("18 kmh"^(-1))`
`"i.e. "t_(1)=(2)/(9)hr=(2)/(9)xx60`
`t_(1)="13.33 "`
(ii) If the two cars are travelling in the opposite direction, relative velocity `vecv_(2)=vecv_(1)+vecv_(2)`
`=72+54 ="126 kmh"^(-1)`
time taken for car A to cross car B `=(4km)/(126km^(-1))=(1)/(31.5)h=(1)/(31.5)xx"60 min"="1.9 min"`