A train leaves the station at 9:00 pm traveling east at 36 miles per hour. A second train leaves the station at 10:00 pm traveling west at 42 miles per hour. At what time will both trains have traveled the same distance? I need help solving it :)
The distance traveled by the 9:00 train from 10:00 onward is
x(9:00) = 36 + 36 * t
Where t is the time in hours after 10:00
The distance traveled by the 10:00 train
from 10:00 onward is
x(10:00) = 42 * t
Set these two equal to each other to find the time at which they have both traveled the same distance
36 + 36*t = 42 * t
36 = 6*t
t = 6 hours
Add 6 hours to 10:00
Simplify the expression.
22+ (32 – 42)
To solve this problem, we need to figure out the time when both trains have traveled the same distance.
Let's assume that the time it takes for both trains to meet is 't' hours after the second train leaves the station.
Since the first train starts an hour earlier, it would have already traveled 36 * t miles when the second train starts.
The second train is traveling in the opposite direction at 42 miles per hour. So, by the time they meet, the second train would have traveled 42 * (t-1) miles.
Now, for both trains to have traveled the same distance, the sum of their distances must be equal at that time.
Therefore, we can set up an equation: 36t = 42(t-1).
Let's solve it step by step:
36t = 42t - 42
42 - 36 = 42t - 36t
6 = 6t
t = 1
So, it will take 1 hour for both trains to meet after the second train leaves the station. Since the second train leaves at 10:00 pm, the trains will meet at 11:00 pm.