A train,after travelling 50 , km,meets with a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the normal speed of the train be $v \, km/hr$.
Let the distance between the point of the first accident $(C)$ and the destination $(B)$ be $d

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) Let the normal speed of the train be $v \, km/hr$.
Let the distance between the point of the first accident $(C)$ and the destination $(B)$ be $d \, km$.
When the accident occurs at $C$,the train travels the remaining distance $d$ at $\frac{3}{4}v$ speed. The time taken is $\frac{d}{\frac{3}{4}v} = \frac{4d}{3v}$.
The time that would have been taken at normal speed is $\frac{d}{v}$.
The delay is $\frac{4d}{3v} - \frac{d}{v} = \frac{d}{3v} = 35 \, minutes = \frac{35}{60} \, hours = \frac{7}{12} \, hours$. So,$\frac{d}{v} = \frac{7}{12} 	imes 3 = \frac{7}{4} \, hours \dots (1)$.
When the accident occurs $72 \, km$ further at $D$,the remaining distance is $(d - 72) \, km$.
The delay is $\frac{d-72}{\frac{3}{4}v} - \frac{d-72}{v} = 15 \, minutes = \frac{15}{60} \, hours = \frac{1}{4} \, hours$.
$\frac{d-72}{v} (\frac{4}{3} - 1) = \frac{1}{4} \implies \frac{d-72}{v} 	imes \frac{1}{3} = \frac{1}{4} \implies \frac{d-72}{v} = \frac{3}{4} \dots (2)$.
Subtracting $(2)$ from $(1)$: $\frac{d}{v} - \frac{d-72}{v} = \frac{7}{4} - \frac{3}{4} = 1 \implies \frac{72}{v} = 1 \implies v = 72 \, km/hr$.

Similar Questions

$A$ truck covers a distance of $550 \, m$ in $1 \, min$,whereas a bus covers a distance of $33 \, km$ in $45 \, min$. The ratio of their speeds is

Walking at three-fourth of his usual speed, a man covers a certain distance in $2 \, \text{hours}$ more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is (in $\text{hours}$):

$A$ bus started its journey from Bettiah and reached Motihari in $44 \, \text{min}$ with an average speed of $50 \, \text{km/h}$. If the average speed of the bus is increased by $5 \, \text{km/h}$, how much time will it take to cover the same distance? (in $\text{min}$)

Two trains,one $160 \, m$ and the other $140 \, m$ long,are running in opposite directions on parallel tracks. The first is moving at $77 \, km/h$ and the other at $67 \, km/h$. How long will they take to cross each other? (in $seconds$)

An express train travelled at an average speed of $100 \, km/hr$, stopping for $3 \, minutes$ after every $75 \, km$. How long did it take to reach its destination $600 \, km$ from the starting point?

Vedclass Test Series

Exam Paper Generator

Online Exam Module