Question #5b908

1 Answer
Feb 2, 2017

The distance is 24 miles.

Explanation:

The basic rule to remember in all problems involving distance, rate and time is:
d=r*t (distance = rate x time)
Beyond that, you need to clearly identify any variables in the equations you write.

We seek the distance in this case, however it is often easier to use a variable for one of the rates (either for the train or driving) or one of the times. This avoids have to change d=rt into a fraction.

Let r= the rate when he is driving (in miles/hr)
Thus r+6=# the rate of the train (in miles/hr)

d=r*t for driving becomes d=r*48
d=r*t for the train becomes d=(r+6)*40
But the distance between home and work is the same in both cases!
So 48r=40(r+6)
48r=40r+240 using the distributive property
8r=240
r=240/8=30 miles/hr

Be careful, though, because the question did not ask for a rate! It asked for the distance.
We have the rate in miles/hour, but we have the time in minutes.
48 minutes = 48/60 hours
30*(48/60)=24 miles using rate * time =distance