Train A and Train B are traveling in the same direction on parallel tracks?

Jon Green: Train A and Train B are traveling in the same direction on parallel tracks?
Train A travels at 80 miles per hour. Train B travels at 100 miles per hour.
Train A passes a station at 5:20am. If train B passes the same station at 5:32am. At what time would Train B catch up to Train A?

Answers and Views:

Answer by deviousatbest
Train B is 12 minutes behind, so it has 12 minutes to make up

The only way it could make it up, is if it traveling at a faster rate, which it is.

So take the difference, 20 mph and find out how long it takes at 20 mph to make up 12 minutes worth of miles at 80 mph

12/60 min = 1/5 x 80 = 16

so you got 16 miles to make up and 20 mph faster rate to do it with

16/20 = 4/5

about 48 minutes

6:20

Answer by Mike
At the time that Train B catches to to Train A they have travelled the same distance.

Calculate the distance for each train individually:

(Rate)(Time) = Distance

Train 1:
(80m/h)(T + 12/60 hr) = Distance
(Note that since the speed is expressed in terms of hours, the 12 minute head start must also be expressed in hours).

Train 2:
(100m/h)(T) = Distance

Now set the two distance equations equal to each other and solve for T:

(80m/h)(T + 12/60 hr) = (100m/h)T
80T + 960/60 = 100T
960/60 = 100T – 80T
16 = 20T
16/20 = T
48/60 = T

So Train B catches Train A in 48/60 hour, or 48 minutes.

48 minutes after 5:32 AM would be

6:20AM.

Answer by Math Wiz
distance = rate * time

Consider the station as being the point t = 0

Let t = the time A travels (from the station)
Let t – 12 = the time B travels (from the station)

Since 12 is minutes, you need to convert the speeds to minutes

80 mph = 80 * 60 mpm = 4800
100 mph = 100 * 60 mpm = 6000

d(Train A) = 4800 * t

d(Train B) = 6000 * (t – 12)

When are the distances the same?

4800 * t = 6000 * (t – 12)

4800t = 6000t – 72000

1200t = 72000

t = 60 minutes

So, when train A is traveling for 60 minutes, the two trains will be at the same point. That occurs at 6:20am.

Check:

At 6:20AM:

Train A has traveled for 60 min (1 hr) at 80 mph, d = 80 miles
Train B has traveled for 48 min (0.8 hrs) at 100 mph, d = 80 miles

CHECK !!!

Answer by Henrik P
d1=d2
d=v*t
v1t1=v2t2, t1=x, t2=x-12/60
80x=100(x-12/60)
20x=20
x=1hour