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A train leaves a town traveling at a speed of 16 mph.

A train leaves a town traveling at a speed of 16 mph. 30 minutes later another train, traveling at 64 mph leaves the same town in the same direction on a parallel track. How long will it take this train to catch up?

Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
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The question you were given is poorly worded.

From the standpoint of the FIRST train, it takes 40 minutes before it is caught.

It only takes the SECOND train, 40-30 = 10 minutes to catch the FIRST train.

I agree that the way the question is worded that it appears to be asking for the 10 minutes, not the 40, but I will show you how to get the "40 minute" answer.

The distance for each train must equal the same for the second train to have "caught up".

Let t be the time in hours that the first train will travel until it is caught.

D1 = (16mph) (t)

The second train will travel for .5 LESS than t hours or t - .5

D2 = (64mph)(t - .5)

D1 = D2

16t = 64t - 32

16t + 32 = 64t

Subtract 16t from both:

32 = 64t - 16t

32 = 48t

Divide both by 48:

32/48 = t

t = 2/3  of an hour or 40 minutes.
Sergey S. | An Author of Computer Programming BooksAn Author of Computer Programming Books
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Let us denote time the second train will travel as X
then the first train will travel X + 0.5 hour.

The distance = speed times time.

Trains catch up when they will travel the same distance.

The First train distance D1= 16mph (X + 0.5)h O.5 hours = 30 minut.
The second train distance D2 = 64mph * X h.

16(X + 0.5) = 64X

16X + 8 = 64X

16X + 8 - 16X = 64X - 16X

8 = 48X X = 1/6 hour or 10 minutes. Answer: 10 min

D1 = 16mph * (30min + 10 min) = 16mph * 0.66 hour = 10.6 miles
D2= 64mph * 1/6h = 10.6 miles

There are 4 possible answers and they are:
- 45 Min
-36 Min
- 60 Min
- 40 Min
Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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From the point of view of the second train, the first catches it up with the speed s=64-16=48 mph. When the second train starts, the first train is 16*0.5=8 miles away. Thus it will take the second train 8/48=1/6 hour or 10 minutes to catch the first train.