Question

Question #5b908

Answer 1

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