Linnear Equations

Question

Two trains are headed towards each other 200 miles apart one train traveling 72 Mph and the second traveling 88mph how long will it take them to collide in hours?

Answer 1

Sadly, I'm not sure how to set up the equations, but, I worked out the answer nonetheless...

 

After an hour, the fast train has traveled 88 miles.

 

After an hour, the slow train has traveled 72 miles.

 

So, after an hour they are only 40 miles apart, because 200 - 72 - 88 = 40

 

After 15 more minutes, the fast train has traveled 22 miles, because 88/60 = 22/15.

 

And, after 15 more minutes, the slow train has traveled 18 miles, because 72/60 = 18/15.

 

So, after 1.25 hours they will crash into each other.

 

OK, here's another way to think about it:

 

The ratio of the trains' speeds is 88/72, so that simplifies to 11/9 or 110/90.  The fast train travels 110 miles at 1 hr/88 miles= 1.25 hours.

 

The slow train travels 90 miles at 1 hr/72 miles = 1.25 hours.

 

 

 

 

 

 

 

 

Answer 2

They both arrive at the same point at the same time t, so

 

200 - 72t = 88t

 

200 = 160t

 

t = 1.25 hours

 

Test the answer.