Expert: Paul Klarreich - 3/13/2008

Question
This is a homework question I received earlier this week. The teacher didn't explain it so that I understood it, so I would just like some help understanding how to do it. Mostly because I thought I understood it in the first place.

Jessica drove to work Tuesday at 40 mph and arrived one minute late. She left home at the same time on Wednesday, drove 45 mph, and arrived one minute early. How far does Jessica drive to work?

I defined my variables as x = distance and y = time.
And my equations x=40(y+1) and x=45(y-1) I got 40 miles. But I know that is wrong somehow. I'd just like help understanding my mistake. Thanks so much

Answer
Questioner:   Charlotte
Category:  Advanced Math
Private:  No
 
Subject:  Algebra - Distance
Question:  This is a homework question I received earlier this week. The teacher didn't explain it so that I understood it, so I would just like some help understanding how to do it. Mostly because I thought I understood it in the first place.

Jessica drove to work Tuesday at 40 mph and arrived one minute late. She left home at the same time on Wednesday, drove 45 mph, and arrived one minute early. How far does Jessica drive to work?

I defined my variables as x = distance and y = time.
And my equations x=40(y+1) and x=45(y-1) I got 40 miles. But I know that is wrong somehow. I'd just like help understanding my mistake. Thanks so much
............................................
Hi, Charlotte,

For starters, I think you are lazy.  Instead of writing:

x = distance [d would be better -- it would remind you what it stands for.]

write

d = the distance driven in miles.

Instead of  

y = time. [t would be better -- it would remind you what it stands for.]

write:

t = the normal time to arrive at work in hours.

Now then,

If you wrote

x = 40(y + 1)

which should be better written as:

d miles = 40 miles per hour(t hours + 1 minute)

you might notice you have a conflict in units.  Hours in one place, minutes in another.  Then you might decide to make them all consistent. You will then have:

d = 40 mph(t hrs + 1/60 hrs.)
d = 45(t - 1/60)  -- likewise.

Yes, fractions are involved.  But make up your mind that fractions are friends and not to be avoided.

Set the two r.h.s.'s equal:

40(t + 1/60) = 45(t - 1/60)

Multiply out:

40t + 40/60 = 45t - 45/60

Reduce:

40t + 2/3 = 45t - 3/4

   2/3 = 5t - 3/4

Clear fractions using LCD = 12 and solve:

   8 = 60t - 9

17 = 60t

t = 17/60 hours.

Go back to find d:

d = 40(17/60 + 1/60)

d = 40(18/60)

d = 4(18/6)

d = 4(3) = 12 miles.