Two trains are travelling on parallel tracks both going from station A to station B.Train 1 leaves at 8 am, at 65 miles per hour. Train 2 leaves at 10 am, at 90 miles per hour. At what time will train 2 catch up to train 1?
5.2 hours later, or
3:12 PM
let the time taken since 10:00 am till they meet be t hrs
at 10:00 am , train will have already gone 130 miles
when they meet, they both will have traveled the same distance, so ...
90t = 130 + 65t
25t = 130
t = 5.2 hrs or 5 hrs and 12 minutes
that would put the time at 10:00 + 5:12
= 17:12 or 5:12 pm
To find out at what time Train 2 will catch up to Train 1, we need to determine the time it takes for Train 2 to cover the distance that Train 1 covers in that time.
Let's say Train 2 catches up to Train 1 after t hours.
To find the distance covered by Train 2 in t hours, we use the formula:
Distance = Speed * Time
For Train 1:
Distance covered by Train 1 = Speed of Train 1 * Time taken by Train 1
Distance covered by Train 1 = 65 mph * t hours
For Train 2:
Distance covered by Train 2 = Speed of Train 2 * Time taken by Train 2
Distance covered by Train 2 = 90 mph * (t - 2) hours
Now, since both the trains cover the same distance when Train 2 catches up to Train 1, we can equate the two distances:
Distance covered by Train 1 = Distance covered by Train 2
65t = 90(t - 2)
Simplify the equation:
65t = 90t - 180
Subtract 65t from both sides:
0 = 25t - 180
Add 180 to both sides:
180 = 25t
Divide both sides by 25:
t = 180 / 25
t = 7.2
Therefore, Train 2 will catch up to Train 1 after 7.2 hours.
To find out the time when Train 2 catches up, we need to add this time to the departure time of Train 1.
Train 1 leaves at 8 am, so we add 7.2 hours to 8 am:
8 am + 7.2 hours = 3:12 pm
Therefore, Train 2 will catch up to Train 1 at 3:12 pm.