Question

Formulate the following problems as a pair of equations, and hence find their solutions :

A train travelled a certain distance at a uniform speed. If the train had been 6 km/hr faster, it would have taken 4 hours less than the scheduled time. If the train were slower by 6 km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train.

Answer 1

Let speed of train be $xkm/hr$.

Let time taken be $yhrs$.

Distance $=xykm$

According to question,

$1stcondition:-$

$(x+6)(y-4)=xy$

$xy-4x+6y-24=xy$

$6y-4x=24$ $-----------\left(1\right)$

$2ndcondition:-$

$(x-6)(y+6)=xy$

$xy+6x-6y-36=xy$

$6x-6y=36$ $-----------\left(2\right)$

On adding $\left(1\right)$ and $\left(2\right)$, we get

$6y-4x+6x-6y=24+36$

$2x=60$

$x=30$

On putting in equation $\left(2\right)$

$6\left(30\right)-6y=36$

$180-6y=36$

$-6y=-144$

$y=24$

So, speed $=30km/hr$

Time $=24hrs$

Distance $=24\times 30=720km$

Hence, this is the answer.