1. ## 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."

2. 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

3. 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 $\displaystyle (distance)=(rate)(time)$.

4. solve $\displaystyle \frac{x+4}{2}=\frac{x}{3}$

5. 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

6. Originally Posted by pickslides
solve $\displaystyle \frac{x+4}{2}=\frac{x}{3}$
should've been, solve $\displaystyle \frac{x-4}{2}=\frac{x}{3}$

7. Got it, thank you all.