Question #5b908

1 Answer
Feb 2, 2017

Answer:

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