Amtrail trains provide efficient, nonstop transportation between Los Angeles and San Diego. Train A leaves Los Angeles headed toward San Diego at the same time that Train B leaves San Diego headed for Los Angeles, traveling on parallel tracks. Train A travels at a constant speed of 84 miles per hour. Train B travels at a constant speed of 92 miles per hour. The two stations are 132 miles apart. How long after they leave their respective stations do the trains meet?
let x be the time taken for them to meet. D=v*t D1=84t, D2=92t The sum of the distances is 132miles.
Thus 84t + 92t = 132
and 176t = 132
or t = 132/176
t =3/4 hours
check:
84(3/4) + 92(3/4)
= 63 + 69
=132 miles
7 hrs
To find out how long it takes for the two trains to meet, we can use the concept of relative speed. Relative speed is the combined speed of two objects moving in the same direction or opposite directions.
In this case, Train A and Train B are moving towards each other on parallel tracks, so we need to find their relative speed.
The relative speed of the two trains can be calculated by adding their individual speeds. In this case, Train A is traveling at 84 miles per hour and Train B at 92 miles per hour, so the relative speed of the two trains is:
84 mph + 92 mph = 176 mph
Now, to determine the time it takes for the trains to meet, we need to divide the distance between the two stations by their relative speed.
Distance between the two stations = 132 miles
Relative speed of the two trains = 176 mph
Time taken for the trains to meet = Distance / Relative speed
Time taken for the trains to meet = 132 miles / 176 mph
Calculating this value:
Time taken for the trains to meet ≈ 0.75 hours
So, the trains meet approximately 0.75 hours (or 45 minutes) after they leave their respective stations.