I'm lost. Please help me solve.
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 miles per hour and train B is traveling at 80 miles per hour. Train A passes a station at 3:25pm. If train B passes the same station at 3:40p.m., at what time will train B catch up with train A?
Train A has a 15 minutes (1/4 hour) "head start". Since it is traveling at 60 miles per hour, it will be how many miles ahead in 1/4 hour? Train B is going 20 miles per hour faster. So, every hour it gains 20 miles on train A.
Calculate how far that train A is ahead.
Calculate how many hours or fraction of an hour it will take train B to catch up since it gains 20 miles every hour. Take that time and add it to 3:40pm to find the time that train B will catch train A.
To solve this problem, we need to calculate the time it takes for train B to catch up with train A.
First, let's find out the time difference between when train A passes the station and when train B passes the station.
Train A passes the station at 3:25 p.m. and train B passes the same station 15 minutes later at 3:40 p.m.
So, the time difference is 15 minutes or 0.25 hours.
Next, we need to calculate the distance that train B needs to cover to catch up with train A.
Since train B starts later, it needs to cover the distance that train A has already traveled.
To calculate this distance, we need to know the time it takes for train B to catch up with train A.
Let's call this time "t" hours.
During this time, train A will have traveled at a speed of 60 miles per hour for "t" hours, covering a distance of 60t miles.
Now, we can set up an equation to find the time "t" it takes for train B to catch up with train A.
Distance covered by train B = Distance covered by train A
80t = 60t + 60t
80t - 60t = 60t
20t = 60t
20t = 0.25
t = 0.25 / 20
t = 0.0125 hours
To convert this time to minutes, multiply it by 60.
0.0125 hours x 60 minutes = 0.75 minutes
Therefore, train B will catch up with train A in 0.75 minutes.
To find out the exact time train B catches up with train A, add this time to the time when train B passes the station, 3:40 p.m.
So, the time when train B catches up with train A is 3:40 p.m. + 0.75 minutes = 3:40 p.m. + 45 seconds.
Therefore, train B will catch up with train A at 3:40 p.m. and 45 seconds.