# Rate problem

• Feb 9th 2009, 07:13 PM
Math Stinks1993
Rate problem
i cant seem to figure this question out could someone tell me the equations for this question please?

In a marathon race. Tom ran part of the 42km at an average of 10k/h and walked the rest at an average 6km/h. he ran for one hour more then he walked. how long did he take to finish the marathon?

fast responde would be greatful thanks :)
• Feb 9th 2009, 07:32 PM
TKHunny
Distance = Rate * Time

That's about it. The rest is a translation exercise. Let's see if we can do it without knowing how long a Marathon is.

"Tom ran part of the 42km at an average of 10k/h"

We are not told the distance, so let's name it. The distance he ran was 'x km'. We are also not told the time, so let's name it. The time he ran for 10 k/h was "w hr".

x km = (10 km/h)*(w hr)

"walked the rest at an average 6km/h."

This time, we have a clue on the distance.

(42 km - x km) = (6 km/h)*???

We also have a clue on the time.

"he ran for one hour more then he walked."

(42 km - x km) = (6 km/h)*((w-1) hr)

"how long did he take to finish the marathon?"

We need ONLY "w" to answer the question.

Let's take a break and see if you get this far. What's next?
• Feb 9th 2009, 07:36 PM
Math Stinks1993
i have no clue on how to solve that lmao...its sooo confusing for me
• Feb 11th 2009, 04:55 PM
TKHunny
1) Get a new screen name. You are very unlikely to succeed with the attitude that is indicated by that name.

2) Get a new attitude. You CANNOT be 100% baffled. It just isn't possible unless you are comatose.

3) Take ONE line at a time. Do NOT move on until you understand each one. You should see that it is a logical progression.

4) There is one abstraction to which you must get accustomed. It is the concept of naming things. When a problem says, "How long did Tommy take to walk to the store?" you should say to yourself, ""I don't know that. I should call that something so I can talk about it." Then write down something like this: "T = The time it took Tommy to walk to the store." After that, you don't have to use the entire phrase; you can just say or write "T". For example, if Jenna takes one hour longer than Tommy to walk to the store, you can describe Jenna's time by the expression "T+1 hr". Another example, if Sujay drives his car, he can get to the store in 1/10 of the time it takes Tommy to make the same trip. You can then describe Sujay's time with "T/10".
• Feb 11th 2009, 07:42 PM
Jhevon
Quote:

Originally Posted by Math Stinks1993
i have no clue on how to solve that lmao...its sooo confusing for me

it helps no one to say this. say specifically what you are having trouble with. re-read post #2 slowly and see if you get it.

another way to look at it (pretty much the same method, but a somewhat different perspective)

Let $x$ be the distance Tom ran
then $42 - x$ is the distance he walked.
Let $t$ be the time Tom ran
then $t - 1$ is the time he walked.

now, you want the sum of the times, that is, he completed the marathon after $t + (t - 1) = 2t - 1$ hours.

so the problem is done once we find $t$.

Now using the equation TKHunny gave: $\text{Time } = \frac {\text{Distance}}{\text{Speed}}$, we have

for running:
$t = \frac x{10}$

for walking:
$t - 1 = \frac {42 - x}6$

you have 2 equations with 2 unknowns, you can solve for t. if you can't, "its sooo confusing for me" is not the correct response.