Question

A car travels from point $A$ to point $B$ with a constant speed. If the driver increased the speed of the car by $6$ km/h, it would take him $4$ hours less to cover that distance. And travelling with the speed $6$ km/h lower than the initial speed, it would take him $6$ hours more. Find the distance between $A$ and $B$.

Answer 1

Let the initial speed be $x$km/hr

let the initial time be $t$ hrs.

Distance is const.

If increased speed by $6$km/hr $t$ decreases by $4$ hours

If decreased speed by $6$km/h, $t$ increases by $6$ hours

$(x+6)(t-4)=(x-6)(t+6)=xt$

$xt-4x+6t-24=xt$

$\underset{–}{xt+6x-6t-36=xt}$

$2x-60=0$

$2x=60$

$x=30$km/hr

$t=24$hours

$xt=720km$