# Basic Math Problem

• Jul 28th 2009, 02:26 PM
mrenvelope
Basic Math Problem
Hello everyone. Can anyone help me solve the following problem or give me an idea where to begin. It seems very basic but I can't seem to work it out. Thank you.

"Mr and Mrs Matrix set out one Sunday to jog round the same course.
Mr Matrix runs 4 km/h faster than his wife. He completes the course in 2 hours and she takes 3 hours.
Calculate how fast each person runs and how long the course is."
• Jul 28th 2009, 02:44 PM
CaptainBlack
Quote:

Originally Posted by mrenvelope
Hello everyone. Can anyone help me solve the following problem or give me an idea where to begin. It seems very basic but I can't seem to work it out. Thank you.

"Mr and Mrs Matrix set out one Sunday to jog round the same course.
Mr Matrix runs 4 km/h faster than his wife. He completes the course in 2 hours and she takes 3 hours.
Calculate how fast each person runs and how long the course is."

Let Dr Matrix run at $\displaystyle m$ km/he, then his wife runs at $\displaystyle (m-4)$ km/h. Let the course length be $\displaystyle l$ km, then:

$\displaystyle 2=l/m$

and:

$\displaystyle 3=l/(m-4)$

Now solve.

CB
• Jul 28th 2009, 02:46 PM
ANDS!
It's not really basic, because you have to figure out what is being said here. To do that lets look at what information we have.

We are told that $\displaystyle \mbox{"Mr. Matrix runs} \ (x+4)\frac{km}{h} \ \mbox{faster than his wife"}.$ We can then allow $\displaystyle x\frac{km}{h}$ to equal the speed of the wife.

We are also told that Mr. Matrix takes 2 hours to complete the course, and the wife takes 3 hours to complete the course. If they are both running the SAME course, then there is an equality here we can exploit using $\displaystyle (distance)=(rate)(time)$.
• Jul 28th 2009, 02:47 PM
pickslides
solve $\displaystyle \frac{x+4}{2}=\frac{x}{3}$
• Jul 28th 2009, 03:32 PM
Krahl
Or....

You could say that in 2 hours mr matrix would accumulate an 8 km gap where he reaches the target. and mrs matrix would need an extra hour to cover 8km.
So she travels at 8km/h and he travels 4km/h faster than this. 12km/h

Pickslides your equation gives -12km/h. i didn't know mr matrix was running backwards. lol joke
• Jul 28th 2009, 03:44 PM
pickslides
Quote:

Originally Posted by pickslides
solve $\displaystyle \frac{x+4}{2}=\frac{x}{3}$

should've been, solve $\displaystyle \frac{x-4}{2}=\frac{x}{3}$
• Jul 28th 2009, 03:47 PM
mrenvelope
Got it, thank you all.(Happy)