If a train runs at 40 kmph it reaches its destination late by 11 minutes. But if it runs at
50 kmph it is late by 5 minutes only. Find the distance to be covered by the train.
Answers
Step-by-step explanation:
Answer:
Given :
Speed of train is \display \text{40 km/hr}\display40 km/hr and its late by 11 min or \displaystyle{\dfrac{11}{60} \ \text{hr}}
60
11
hr .
In other case it's also given speed of train is \display \text{50 km/hr}\display50 km/hr and late by 5 min or \displaystyle{\dfrac{5}{60} \ \text{hr}}
60
5
hr .
Let the train covered 'd' km distance.
The journey let it took 't' hr time.
We have difference in late of time i.e.
\displaystyle{\dfrac{11}{60} -\dfrac{5}{60}=\dfrac{1}{10}}
60
11
−
60
5
=
10
1
We know ,
\display \text{Time = $\dfrac{\text{Distance}}{\text{Speed}}$}\displayTime =
Speed
Distance
A.T.Q.
\begin{gathered}\displaystyle{\frac{\text{d}}{40} -\frac{\text{d}}{50}= \frac{1}{10}}\\\\\\\displaystyle{\dfrac{\text{d}}{10}(\frac{1}{4} -\frac{1}{5})= \frac{1}{10}}\\\\\\\displaystyle{\text{d}(\dfrac{1}{20})=1}\\\\\\\displaystyle{\text{d}=20 \ \text{km}}\end{gathered}
40
d
−
50
d
=
10
1
10
d
(
4
1
−
5
1
)=
10
1
d(
20
1
)=1
d=20 km
Hence , the distance to be covered by the train is 20 km .
Let the normal time be ‘t’ hours to reach the destination at a distance of ‘x’ km
If the train runs at 40 km/hr it reaches the destination , the train is late by 11 minutes , i.e late by 11/60 hours, Ot it takes t + 11/60 hours. Then
Distance = Speed x time
i . e x = 40 *(t+11/60) ……….(1)
Again when the train runs at a speed of 50 km/he , it reaches 5 minutes late. So we have the following equation as well
i.e. x = 50 * ( t+ 5/60) …………. (2)
Equating equation (1) and (2), now we have this expression
40*(t+11/60) = 50(t+5/60)
4(t+11/60) = 5(t+5/60)
4t + 11/15 = 5t + 5/12
t = 11/15 - 5/12
t = (132 - 75)/180
t = 57/180
t = (57/180)*60 minutes
t = 19 minutes
If it runs at 40 km per hour , it reaches late by 11 minutes , it takes 19+11 = 30 minutes which means 30/60 = 1/2 hour
Therefore x = 40*(1/2 )= 20 kms
Hence normal speed is 20/(19/60)
= 63.15789 km/h
Hence at a speed of 63.15789 km/hr, the train will reach the destination in 19 minutes
( at 40 km/hr the train will reach in 19+11 = 30 minutes , and at 50km/hr , the train will reach in 19+5 = 24 minutes)
Hence , the normal time without being late is 19 minutes
BHUT TIME LAGA BRANLIST MARK KARDOON