Word problem

Question

Two trains traveling on parallel tracks are going toward each other from a distance of 623 miles. If the freight train is moving at 42 mph and the passenger train is moving at 47 mph, when will the trains pass each other?

Answer 1

Always think of these problems as an equation.  What are we trying to figure out?  Time in hours.  That should be our x variable.  Ok, what do we know?  One train is going one direction, and the other is going the opposite direction.  623 is our nonvariable distance.  You can put the numbers in any position you like, as long as one is positive and the other is negative to denote the opposite directions.  Look at my solution below:

 

47x = 623 - 42x

 

623 miles = 89 mph * x

 

x = 623/89 hours = 7 hours

 

Not too bad when you spend the time to think about it!  Give it a try!

Answer 2

Hi Lisa,

 

Speed = distance / time.  As you want to figure out the time, the equation will be rewritten as:

 

time = distance / speed

 

Passenger train is going 47 mi/hr and Freight train is going 42 mi/hr.

 

47t + 42 t = 623

 

(You can put both positive if you put each train at opposite starting point and each train is traveling positive direction respect to their starting point.  But if you set starting point and end point respect to only one train, then one of them will be negative.)

 

If you set both to positive:

 

47t + 42 t = 623   (t = time)   89t = 623     t = 7 hours

 

47(7) + 42(7) = 329 + 294 = 623

 

If you set one of them to negative:

 

0 + 47t = 623 - 42t

 

(Negative sign is for traveling opposite direction)

(This is due to setting the starting point respect to only 1 train)

 

If you set one at 0 and the other one at 623, one that is at 623 will travel negatively because it is traveling towards zero: one will travel 0 to 623 (+) and the other one will travel 623 to 0 (-).

 

0 + 47t = 623 - 42t   (0 for one train and 623 for the other train)

 

42t + 47t = 623     89t = 623     t = 7 hours

 

Good luck to you.