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  • A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled tim

Q3. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Answers (1)

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Let the speed of the train be v km/h, the time taken by train to travel the given distance be t hours and the distance to travel be d km. 

Now, as we Know,

speed=\frac{distance }{time}

\Rightarrow v=\frac{d}{t}


\Rightarrow d=vt..........(1)
Now, according to the question,
 (v+10)=\frac{d}{t-2}

\Rightarrow (v+10){t-2}=d

\Rightarrow vt +10t-2v-20=d

Now, using equation (1), we have 

\Rightarrow -2v+10t=20............(2)
Also,

(v-10)=\frac{d}{t+3}

\Rightarrow (v-10)({t+3})=d

\Rightarrow vt+3v-10t-30=d
 \Rightarrow3v-10t=30..........(3)

Adding equations (2) and (3), we obtain:
v=50.
Substituting the value of x in equation (2), we obtain:
(-2)(50)+10t=20

\Rightarrow -100+10t=20

\Rightarrow 10t=120

\Rightarrow t=12
Putting this value in (1), we get:

d=vt=(50)(12)=600

Hence, the distance covered by train is 600km.

Posted by

Pankaj Sanodiya

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