A car traveling 50 mph goes 15 miles farther in the same amount of time as a car traveling 30 mph. Find the distance that each car has traveled. (hint: d=rt)

Question

I am having a lot of trouble with this question. it is due by tomorrow so if you are reading this and it's past 8:00 on March 29th 2015 you don't have to answer

Answer 1

This is a problem about finding the intersect of linear equations. So, if we consider the distance traveled by car one as a function of time,

    d(t) = speed *  t

then we have 

    d1( t ) = 50 *  time
    d2( t ) = 30 *  time

We are looking for a specific case with these. We can the point where the distance traveled by the first car (d1) is 15 miles greater than the distance traveled by the second car (d2)

    d1( t ) = d2 ( t ) + 15

If we take the equations for d1 and d2, and substitute them in, then we get (including units now)

    50 m/hr * t hr = 30 m/hr * t hr + 15 m

which we solve with a bit of algebra (solve for t).

    50 m/hr * t hr - 30 m / hr * t hr = 30 m/hr * t hr - 30 m/hr * t hr  + 15 m

    ( 50 m/hr  - 30 m / hr ) * t hr = ( 30 m/hr * t hr - 30 m/hr * t hr ) + 15 m

    (20 m / hr) * t hr = 0 + 15 m

    20 m / hr * t hr =15 m
    t hr = (15 m ) / (20 m / hr )

    t hr = (15 m * hr ) / 20 m

    t hr = (15 / 20 ) hr
    t = .75 hr = 45 minutes

Answer 2

distance = rate*time.  Let x = the distance traveled by the car going 30 mp:

x = 30*time

 

The car going 50 mph goes 15 miles further in the same time:

 

x + 15 = 50*time

 

Since x = 30*time:

 

(30*time) + 15 = 50*time

15 = 20*time

15/20 = time

(3/4) hour = time = 45 minutes

 

Check:

d = 30*(3/4) = 22.5 miles

d = 50*(3/4) = 37.5 miles

 

37.5 - 22.5 = 15 miles

 

Check!