If a train runs at 40 text{ km/h},it reaches | vedclass

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Question

(A) Let the distance be $d 	ext{ km}$ and the scheduled time be $t 	ext{ minutes}$.When the speed is $40 	ext{ km/h}$,the time taken is $\frac{d}{4

Vedclass · Accepted Answer

$19$

Vedclass · Answer

(A) Let the distance be $d 	ext{ km}$ and the scheduled time be $t 	ext{ minutes}$.When the speed is $40 	ext{ km/h}$,the time taken is $\frac{d}{40} 	ext{ hours} = \frac{60d}{40} 	ext{ minutes} = 1.5d 	ext{ minutes}$.Given that the train is $11 	ext{ minutes}$ late,we have: $1.5d = t + 11$ ... $(1)$When the speed is $50 	ext{ km/h}$,the time taken is $\frac{d}{50} 	ext{ hours} = \frac{60d}{50} 	ext{ minutes} = 1.2d 	ext{ minutes}$.Given that the train is $5 	ext{ minutes}$ late,we have: $1.2d = t + 5$ ... $(2)$Subtracting equation $(2)$ from equation $(1)$:$(1.5d - 1.2d) = (t + 11) - (t + 5)$$0.3d = 6$$d = \frac{6}{0.3} = 20 	ext{ km}$.Substituting $d = 20$ into equation $(1)$:$1.5(20) = t + 11$$30 = t + 11$$t = 30 - 11 = 19 	ext{ minutes}$.Thus,the correct time is $19 	ext{ minutes}$.

If a train runs at $40 \text{ km/h}$,it reaches its destination late by $11 \text{ minutes}$,but if it runs at $50 \text{ km/h}$,it is late by $5 \text{ minutes}$ only. Find the correct time for the train to complete its journey (in minutes).

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