Train A leaves Tigerville at 9 am traveling east at 85 mph. Train B leaves Liontown at 9:20am travelling west at 60 mph on the exact same tracks. Tigerville and liontown are 154 miles apart. At what time will the trains meet?
When they "meet" the difference in their travel time is 20 minutes or 1/3 of an hour
let the distance from from Tigersville be x
x/85 - (154-x)/60 = 1/3
times 1020 , the LCM of 85, 60 and 3
12x - 17(154-x) = 340
12x - 2618 + 17x = 340
29x = 2958
x = 102
time for first train = 102/85 = 1.2 hrs or 72 minutes
time for 2nd train = (154-102)/60 = 52 minutes
so they will meet at 9:00 am +72 min
= 10:12 am
To find the time when the trains meet, we need to determine the time it takes for Train B to travel the distance between Tigerville and Liontown.
First, we need to determine the time difference between Train A and Train B. Train B leaves 20 minutes (or 1/3 hour) after Train A.
Next, we calculate the distance Train A travels before Train B starts. Since they travel in opposite directions, the total distance between Tigerville and Liontown, which is 154 miles, is divided between them.
Train A travels for 1/3 hour before Train B starts, so we calculate its distance traveled as (1/3) * 85 mph = 28.33 miles.
Train B has to travel the remaining distance of 154 - 28.33 = 125.67 miles.
To find the time it takes for Train B to travel this distance, we divide the distance by its speed: 125.67 miles / 60 mph = 2.0945 hours.
Since Train B leaves at 9:20 am, we add 2.0945 hours to this time to calculate when the trains will meet:
9:20 am + 2.0945 hours = 11:18 am
Therefore, the trains will meet at approximately 11:18 am.