SOLUTION: Car 1 travels from point A to point B.. Car 2 leaves 2 hours later, but goes 10 miles an hour faster and passes car 1 in 11 hours.. How fast does each car go??

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Car 1 travels from point A to point B.. Car 2 leaves 2 hours later, but goes 10 miles an hour faster and passes car 1 in 11 hours.. How fast does each car go??      Log On


   

Question 514496: Car 1 travels from point A to point B.. Car 2 leaves 2 hours later, but goes 10 miles an hour faster and passes car 1 in 11 hours.. How fast does each car go??
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Car 1 travels from point A to point B.. Car 2 leaves 2 hours later, but goes 10 miles an hour faster and passes car 1 in 11 hours.. How fast does each car go??
Make this chart

        Distance      Rate     Time 
Car 1   
Car 2   


Let x = the rate of Car 1

Car 2...goes 10 miles an hour faster
So the rate of Car 2 = x+10

Fill those rates in:

        Distance      Rate     Time 
Car 1                   x       
Car 2                 x+10

Car 2...passes car 1 in 11 hours
So fill in 11 for Car 2's time:

        Distance      Rate     Time 
Car 1                   x       
Car 2                 x+10      11

Car 2 leaves 2 hours later
This means Car 1 traveled 2 hours longer than Car 2,
so Car 1's time is 11+2 = 13.  Fill that in for 
Car 1's time.

        Distance      Rate     Time 
Car 1                   x       13
Car 2                 x+10      11

Now we use the formula Distance=Rate%2ATime to fill
in the distances:

        Distance      Rate     Time 
Car 1      13x          x       13
Car 2   11(x+10)      x+10      11


Now the distances traveled by each car are the same,
so we set the two distances equal:

           13x = 11(x+10)

Solve that equation for x and get x = 55 mph for Car 1.  
Car 2 went 10 mph faster, so it went 65 mph.

Edwin