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### Two-equation Rate Problem

```
Date: 09/26/1999 at 18:14:46
From: Andrew
Subject: Algebra II with Trigonometry

On a recent trip, Ellie drove 264 km in the same time that Carol took
to drive 198 km. Ellie's speed was 17 km greater than Carol's speed.
Find the rate of each.

For this, so far I know you have to set up 2 equations. I let
E = Ellie and C = Carol. I have one easy equation of E = C+17 and I
can't find the other equation. How do I do this?
```

```
Date: 09/29/1999 at 11:31:22
From: Doctor Rick
Subject: Re: Algebra II with Trigonometry

Hi, Andrew.

Yes, the second equation is harder. You need to use the rate equation.
First, let me spell out in more detail what your variables are - it's
good to be really clear:

E = Ellie's speed in km/hour
C = Carol's speed in km/hour

(I assume you meant km/hour rather than km, which is not a speed,
though we do often talk this way.)

How long does it take Ellie to drive 264 km? We know that

distance = rate * time

time = distance / rate

time = (264 km) / (E km/hour)
= (264/E) hours

How long does Carol take to drive 198 km? Setting these times equal
will give you your second equation.

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