SOLUTION: How would you write this problem? I know once it is written that way, I can solve it. I just don't know how to format it. Susan types 75 words per minute and is just starting

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Question 812722: How would you write this problem? I know once it is written that way, I can solve it. I just don't know how to format it.
Susan types 75 words per minute and is just starting to write a term paper. Paul already has 510 words written and types at a speed of 60 words per minute. For what numbers of minutes will Susan have more words typed than Paul?
Found 3 solutions by richwmiller, josgarithmetic, MathTherapy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Isn't the question backwards?
Paul already has 510 words typed but types slower than Susan.
This is similar to the car chase problems.
Susan types 15 words a minute faster than Paul
It will take 34 minutes for Susan to catch up with them both typing.
Paul will be ahead for 34 minutes. 510/15=34
If Paul stopped typing it would take only 6.8 minutes to catch him
510/75 =6.8
It took Paul 8.5 minutes 510/60 to type those 510 words.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates problem.

R is in words per minute;
t is in minutes;
w is in words.
Rt=w

Reading the description, at some time, w will be equal for both people, but one has already more words than the other. Susan must type w words (now assigning a variable), and Paul must still type w-510.

Try a data table:

Typist_________rate___________time___________words
Susan__________75_____________t______________w
Paul___________60_____________t_____________w-510

Each would type for the same amount of time, according to the data tabulated information and the inferred assigning of t. The number of words will be different for each during time t. Reason is Paul already has some words printed.

We would want to first solve for w. HOW? Use R*t=w, and divide both sides by R.
We have t=w%2FR

Our data table may look like this:

Typist_________rate___________time___________words
Susan__________75_____________t=w%2F75______________w
Paul___________60_____________t=%28w-510%29%2F60_____________w-510

Can you see what to do? The times, "t" are equal. Find the value for w. You plainly have two formulas for t.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
How would you write this problem? I know once it is written that way, I can solve it. I just don't know how to format it.
Susan types 75 words per minute and is just starting to write a term paper. Paul already has 510 words written and types at a speed of 60 words per minute. For what numbers of minutes will Susan have more words typed than Paul?

It'll take her highlight_green%2835%29 minutes to type more words than Paul, if he continues typing after typing 510 words. At their rates, they will have typed 2,550 words in 34 minutes.

You can do the check!!

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