What Time Does She Get to Work?

Date: 04/30/2002 at 17:25:59
From: David Williams
Subject: Distance vs. time

Lillian drives to work at an average speed of 45 miles per hour. If 
she travels 30 miles to work and leaves at 8:00 A.M., what time does 
she get to work?

Please help me - I really don't know what I'm doing.

Date: 05/01/2002 at 11:09:29
From: Doctor Ian
Subject: Re: Distance vs. time

Hi David, 

The first step in solving a problem is to identify what you want to 
know. In this case, you want to know when Lillian gets to work. 

You could figure that out if you knew how long it takes her to drive 
to work.  

So what you're _really_ trying to find out is how long it takes to 
drive 30 miles at 45 miles per hour. Now, let's say that it takes H 
hours to drive 30 miles at 45 miles per hour:

    H  =>  30 miles at 45 miles per hour

If you drive twice as fast, it will take half as long:

  H/2  =>  30 miles at 90 miles per hour

If you drive 3 times as far, it will take three times as long:

 3H/2  =>  90 miles at 90 miles per hour

But 90 miles at 90 miles per hour should take exactly one hour, right?  
So 

  3H/2 = 1 hour

Now, there is a shorter way to do it, which is to use the formula

   distance = rate * time

   30 miles = 45 miles/hour * ? hours

and solve for the '?'. But the problem with formulas is that they're 
easy to forget, which is why it's good to know how to do it the other 
way, too. It's like knowing two ways to get home, in case one of them 
is blocked for some reason. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/