SOLUTION: Train A & B are traveling in the same direction on parallel track. Train A is traveling 80 miles per hour and train B is traveling 90 miles per hour. Train A passes station at 3:10

Question 280838: Train A & B are traveling in the same direction on parallel track. Train A is traveling 80 miles per hour and train B is traveling 90 miles per hour. Train A passes station at 3:10 pm If train B passes same station at 3:22 pm what time will train B catch up to train A
Found 3 solutions by stanbon, Alan3354, josmiceli:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Train A & B are traveling in the same direction on parallel track.
Train A is traveling 80 miles per hour and train B is traveling 90 miles per hour.
Train A passes station at 3:10 pm If train B passes same station at 3:22 pm what time will train B catch up to train A?
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Train A DATA:
rate = 80 mph ; time = x hrs ; distance = rt = 80x miles
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Train B DATA:
rate = 90 mph ; time = (x-(12/60)) hrs ; distance = 90(x-(1/5)) miles
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Equation:
distance = distance
80x = 90x - 18
10x = 18
x = 1.8 hrs = 1 hr 48 minutes
===================================
Cheers,
Stan H.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Train A & B are traveling in the same direction on parallel track. Train A is traveling 80 miles per hour and train B is traveling 90 miles per hour. Train A passes station at 3:10 pm If train B passes same station at 3:22 pm what time will train B catch up to train A
--------------------
at 322, train A is 16 miles from the station (80 mph * 12/60)
Train B gains on train A at 10 mph (90 - 80)
16 miles at 10 mph --> 1.6 hours or 1 hr 36 minutes
322 + 136 = 4:58 PM

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
I have a stopwatch.
I'll start it when the 2nd train, train B, passes the station
Train A passed the station 12 min ago at 3:10
How far did train A get in 12/60 hr? That is his headstart
mi
Now write equations for each train, with time = for both,
since I'll stop the stopwatch when they meet

Also note that
Substituting:
(1)
(2)
Substituting again:

hr
B will catch A in 1 hour 36 min, or at 3:22 + 1:36 = 4:58 PM
check:

OK
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