How Do I Solve Problems Like These?

Question

At 9:00 A.M. two trains leave from towns that are 200 miles apart and head toward each other. One train travels at a constant 48 mph while the other travels at a constant 52 mph. At what time do the trains meet?

 

Answer 1

The two trains are 200 miles apart. So, the combined distance they must travel is 200 miles.

Both trains are traveling at constant speeds, and they travel the same length of time.

For either train, the distance it travels is

speed x time. Using t as the variable for time

For train 1, the distance it travels is

48t

For train 2, the distance it travels is

52t

 

Since the 2 trains meet when the distance traveled is 200 miles, and since they both travel the same length of time t,

48t + 52t = 200

100t = 200

t = 2 hours

 

So, the trains meet after 2 hours, or at 11 am

Answer 2

This is the standard rate problem of d=rt

 

For the first train the rate is 48 m/hr. The second train is 52 m/hr. Though their rates are different the time they travel, t is the same. The distances are different. But if train 1 travels d train 2 will travel 200-d

 

t=d/48=(200-d)/52 hrs 

 

solving for d. First cross-multiply to get rid of the fractions.

52d=48(200-d)

100d=9600

d=96 miles

 

The time for train one

t=96/48=2 hours

 

The distance for train two is

dd=200-96=104 miles

 

The time for train two is

t=104/52=2 hours

 

Thats a good check they should both travel the same amount of time. We need to add two hours to their departure time of 9 am to get the time they meet.

 

They meet at 11 am.