without stoppage a train travels a distance with an average speed of 60 km/hr and with stoppage it covers the same distance with an average speed of 40 km/hr. on an average how many min per hour does the train stop during the journey.
let the travel time be t hrs
let the stoppage time be s hrs
without stopping, distance = 60t
with stops, distance = 40(t+s)
60t = 40t + 40s
20t = 40s
t = 2s
So for any given time, the train spends twice the time driving as it does stopping
or
in hour , the time stopping is 20 minutes and the time driving is 40 minutes.
let's take some cases to illustrate:
suppose the distance is 240 km
time without stopping = 4 hrs
time with stops = 6 hours
time spend on stops = 2 hrs, which is 1/2 of the time driving
suppose the distance is 600 km
time without stops = 10 hours
time with stops = 15 hours
time spent on stops = 5 hours, which is 1/2 of the time driving
To find out how many minutes per hour the train stops during the journey, we need to first determine the time it takes to cover the distance with and without stoppage.
Let's assume the distance covered by the train is "D" kilometers.
Without stoppage:
To find the time taken without stoppage, we use the formula: Time = Distance / Speed.
So, the time taken without stoppage = D km / 60 km/hr = D/60 hours.
With stoppage:
Similarly, to find the time taken with stoppage, we use the formula: Time = Distance / Speed.
So, the time taken with stoppage = D km / 40 km/hr = D/40 hours.
The difference in the time taken with and without stoppage will give us the time the train stops during the journey:
Time stopped = Time taken without stoppage - Time taken with stoppage
= (D/60) - (D/40)
= D(1/60 - 1/40)
= D(1/60 - 3/120)
= D(1/60 - 1/40)
= D/120 hours.
Now, we need to find the time stopped in minutes per hour. As there are 60 minutes in an hour, we can multiply the time stopped by 60 to get the time stopped in minutes.
Time stopped in minutes = (D/120) * 60
= (D * 60)/120
= D/2 minutes per hour.
Therefore, on average, the train stops for D/2 minutes per hour during the journey.