If I walk at 5, km/hr,I miss a train by 7, mi | vedclass

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

Question

(A) Let the distance between the house and the station be $D\, km$ and the scheduled time of the train be $T\, hours$.When walking at $5\, km/hr$,the

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Let the distance between the house and the station be $D\, km$ and the scheduled time of the train be $T\, hours$.When walking at $5\, km/hr$,the time taken is $\frac{D}{5}$ hours. Since $I$ miss the train by $7\, minutes$ $(7/60\, hours)$,the time taken is $T + 7/60$.So,$\frac{D}{5} = T + \frac{7}{60} \implies T = \frac{D}{5} - \frac{7}{60} \dots (1)$When walking at $6\, km/hr$,the time taken is $\frac{D}{6}$ hours. Since $I$ reach $5\, minutes$ $(5/60\, hours)$ early,the time taken is $T - 5/60$.So,$\frac{D}{6} = T - \frac{5}{60} \implies T = \frac{D}{6} + \frac{5}{60} \dots (2)$Equating $(1)$ and $(2)$:$\frac{D}{5} - \frac{7}{60} = \frac{D}{6} + \frac{5}{60}$$\frac{D}{5} - \frac{D}{6} = \frac{5}{60} + \frac{7}{60}$$\frac{6D - 5D}{30} = \frac{12}{60}$$\frac{D}{30} = \frac{1}{5}$$D = \frac{30}{5} = 6\, km$Thus,the distance is $6\, km$.

If $I$ walk at $5\, km/hr$,$I$ miss a train by $7\, minutes$. However,if $I$ walk at $6\, km/hr$,$I$ reach the station $5\, minutes$ before the departure of the train. The distance between my house and the station is (in $km$)

Similar Questions

$A$ man covered a certain distance at some speed. Had he moved $3 \text{ km/hr}$ faster,he would have taken $40 \text{ minutes}$ less. If he had moved $2 \text{ km/hr}$ slower,he would have taken $40 \text{ minutes}$ more. The distance (in $\text{km}$) is:

$A$ train crosses a pole in $10 \, s$ and a platform,which is $40 \%$ longer than the length of the train,in $24 \, s$. If the length of the platform is $140 \, m$,what is the speed of the train in $m/s$?

$A$ train $100 \, m$ long takes $3 \frac{3}{5} \, s$ to cross a man walking at the rate of $6 \, km/h$ in a direction opposite to that of the train. Find the speed of the train in $km/h$.

$A$ person sets out to cover a distance of $12 \, km$ in $45 \, minutes$. If he covers $\frac{3}{4}$ of the distance in $\frac{2}{3}$ of the time,what should be his speed to cover the remaining distance in the remaining time? (in $km/h$)

$A$ train covers a distance of $10 \text{ km}$ in $12 \text{ minutes}$. If its speed is decreased by $5 \text{ km/hr}$,the time taken by it to cover the same distance will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module