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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.

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Solution

Let speed of train be x km/hr.
Let time taken be y hrs.
Distance =xy km

According to question,

1st condition :
(x+6)(y4)=xy
xy4x+6y24=xy
6y4x=24 (1)

2nd condition :
(x6)(y+6)=xy
xy+6x6y36=xy
6x6y=36 (2)


On adding (1) and (2), we get
6y4x+6x6y=24+36
2x=60
x=30

On putting in equation (2)
6(30)6y=36
1806y=36
6y=144
y=24

So, speed =30 km/hr
Time =24hrs
Distance =24×30=720 km

Hence, this is the answer.

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