A train leaves the station at noon. The train is 180mi from its destination at 12:45PM and 90mi from the destination at 2:15PM.
1. How far is the station from the destination?
2. At what time will the train reach the destination?
assume that the train travels at a uniform rate.
between 12:45 and 2:15 ---> 1.5 hrs
the train went 90 miles
rate = 90/1.5 or 60 mph
now use a simple ratio, if x is the distance traveled from noon to 12:45
x/.75 = 90/1.5
x = .75(90/1.5) = 45 miles
but the train at this point has 180 miles to go, so
the distance from the station to the destination is 225 miles
time to go 225 miles at 60 mph
= 225/60 =3.75 hr
which would make it 3:45 pm
To find the distance between the station and the destination, we can subtract the distance the train has traveled from the total distance of the journey.
1. Distance between the station and the destination:
Total distance of the journey = 180 mi (from 12:00 PM to 12:45 PM) + 90 mi (from 12:45 PM to 2:15 PM) = 270 mi
Distance between the station and the destination = Total distance of the journey - Distance traveled = 270 mi - 90 mi = 180 mi
Therefore, the station is 180 miles from the destination.
To determine the time when the train will reach the destination, we need to calculate the average speed of the train.
2. Average speed of the train:
Speed = Distance / Time
Speed from 12:00 PM to 12:45 PM = 180 mi / 45 min = 4 mi/min
Speed from 12:45 PM to 2:15 PM = 90 mi / 90 min = 1 mi/min
To calculate the total time of the journey, we need to know the remaining distance and the speed of the train.
Remaining distance = Distance between the station and the destination = 180 mi
Speed of the train = Average speed = (4 mi/min + 1 mi/min) / 2 = 2.5 mi/min
Time to reach the destination:
Time = Distance / Speed
Time = 180 mi / 2.5 mi/min = 72 min = 1 hour and 12 minutes
Therefore, the train will reach its destination at 2:27 PM (12:00 PM + 1 hour and 27 minutes)