1. ## Rates

Hi,

I just have some niggling doubts on solving these problems. I'm aware of the method of 'picking numbers', but I seek a more general understanding. Could someone explain to me how to solve these problems generally? Or how to think of them.

1.) Bill has to type a paper that is $p$ pages long, with each page containing $w$ words. If Bill types an average of $x$ words per minute, how many hours will it take him to finish the paper?

(A.) $60wpx$

(B.) $\frac{wx}{60p}$

(C.) $\frac{60wp}{x}$

(D.) $\frac{wpx}{60}$

(E.) $\frac{wp}{60x}$

Answer: (E.) $\frac{wp}{60x}$

2.) If David paints at the rate of $h$ houses per day, how many houses does he paint in $d$ days, in terms of $h$ and $d$?

Answer: $hd$

2. Originally Posted by Hellbent
Hi,

I just have some niggling doubts on solving these problems. I'm aware of the method of 'picking numbers', but I seek a more general understanding. Could someone explain to me how to solve these problems generally? Or how to think of them.

1.) Bill has to type a paper that is $p$ pages long, with each page containing $w$ words. If Bill types an average of $x$ words per minute, how many hours will it take him to finish the paper?

(A.) $60wpx$

(B.) $\frac{wx}{60p}$

(C.) $\frac{60wp}{x}$

(D.) $\frac{wpx}{60}$

(E.) $\frac{wp}{60x}$

Answer: (E.) $\frac{wp}{60x}$

2.) If David paints at the rate of $h$ houses per day, how many houses does he paint in $d$ days, in terms of $h$ and $d$?

Answer: $hd$
1) How many words does Bill have to type? Divide this by Bills word per minute rate to get the how many minutes it will take him ....

2) You're given the answer. Think it over ....

3. Originally Posted by mr fantastic
1) How many words does Bill have to type? Divide this by Bills word per minute rate to get the how many minutes it will take him ....

2) You're given the answer. Think it over ....
It's a multiple choice question. The options are:

(A.) $\frac{h}{d}$

(B.) $hd$

(C.) $h + \frac{d}{2}$

(D.) $h - d$

(E.) $\frac{d}{h}$

It's $hd$. Try picking numbers for h and d. h = 4; d = 5. He paints 4 houses a day and he paints for 5 days he can paint 20 houses.
Multiplying the rate (h) by the number of days (d). Plugging in the respective values for $h$ and $d$, only one gives 20. This is just following the 'pick numbers' method. The book also gives this answer.

4. Originally Posted by Hellbent
It's a multiple choice question. The options are:

(A.) $\frac{h}{d}$

(B.) $hd$

(C.) $h + \frac{d}{2}$

(D.) $h - d$

(E.) $\frac{d}{h}$

It's $hd$. Try picking numbers for h and d. h = 4; d = 5. He paints 4 houses a day and he paints for 5 days he can paint 20 houses.
Multiplying the rate (h) by the number of days (d). Plugging in the respective values for $h$ and $d$, only one gives 20. This is just following the 'pick numbers' method. The book also gives this answer.
Part of thinking the answer over is to look at the unit of h and d and, perhaps, draw the obvious conclusion.