Question 972254: Three trains start at different times on a 100 mile journey.Train A leaves late and stops at a station for 5 minutes.its average speed is 40mph.Train B leaves 20 minutes late and stops at a station for 14 minutes. its average speed is 50mph. Train c leaves 30 minutes late and stops at a station for 10 minutes.its average speed is 50mph.which train completes the journey in the shortest time
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there may be a few ways to calculate this.
let's try this one.
train B.
when it is moving, train B travels at 50 mph.
100 miles divided by 50 miles per hour is 2 hours.
train B left 20 minutes late and stopped at a station for 14 minutes.
20 + 14 = 34 minutes divided by 60 minutes per hour = 34/60 hours
take 2 hours and add 34/60 hours and you get 2 hours and 34/60 hours total time for train B to travel 100 miles.
this is equivalent to 2.57 hours.
train C.
when it is moving, train C travels at 50 mph.
100 miles divided by 50 miles per hour is 2 hours.
train C left 30 minutes late and stops at a station for 10 minutes.
30 + 10 = 40 minutes divided by 60 minutes per hour = 40/60 hours.
take 2 hours and add 40/60 hours and you get 2 hours and 40/60 hours total time for train C to travel 100 miles.
this is equivalent to 2.67 hours.
so far train B took less time overall.
train A.
train A leaves late, but you haven't said how late.
that's a missing point of information for train A.
it stops at a station for 5 minutes.
it's average speed is 40 mph, when it is moving!!!!!
this is a key assumption.
average speed when it is moving is different than average speed overall.
average speed overall includes the time it is not moving.
the train that takes the longest time will have the lowest overall speed regardless of what speed it is traveling at when it is moving.
train A would take 100/40 = 2.5 hours without any stops and without being late.
train A stopped at a station for 5 minutes, so the total time it takes without being late is 2.5 + 5/60 hours.
this is equivalent to 2.58 hours.
you still need to add x hours to this for the number of hours that train A is late.
it doesn't matter.
even if train A left on time, it would not have the fastest time overall.
based on this analysis, train B takes the shortest time at 2.57 hours.
train A, even if it was not late starting, took 2.58 hours.
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