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

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Solution

Let the distance covered by the train $= d$ km and speed $= s$ km/hr.
Distance $=$ Speed $\times$ Time $=$ constant
where, Time is in hrs
$s t = (s + 10) (t - 2)$ ......(i)
$s t = (s - 10) (t + 3)$ .....(ii)
Simplifying the (i), $s t = s t - 2 s + 10 t - 20$
$\Rightarrow 2 s - 10 t = - 20$ .....(iii)
Simplifying the (ii) we get, $s t = s t + 3 s + 10 t - 30$
$\Rightarrow 3 s - 10 t = 30$ ............(iv)
Multiplying (iii) by $3$ & (iv) by $2$ , we get
$6 s - 30 t = - 60$ ..........(v)
$6 s - 20 t = 60$ .......... (vi)
Subtracting equation (vi) from (v), we get
$- 10 t = - 120 t = 12 h r s$
Putting the value of $t$ in equation (iii),
$s = 50 k m / h r$
$d = s t = 50 \times 12 = 600$ km

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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 time. Find the distance covered by the train.

a train covered A certain distance at a uniform speed if the train would have been 10 km per hour faster it would have taken 2 hours less than the scheduled time and the train was lower by 10 km per hour it would have taken 3 hours more than the scheduled time find the distance covered by the train

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