We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

My friend and I both have the same math homework one day. I work at a rate of p problems per hour and it takes me t hours to finish my homework. My friend works at a rate of 2p-4 problems per hour and it only takes him t-2 hours to finish his homework. Given that p and t are positive whole numbers and I do more than 10 problems per hour, how many problems did I do?

xXxTenTacion Jul 4, 2018

#1**+1 **

What do you mean by " and I do more than 10 problems per hour"? Your stated rate is p problems per hour! Unless you mean your rate is "p + 10". You have to clarify it. There are many different solutions, but not a unique one as the problem is stated.

Guest Jul 4, 2018

#2**+1 **

I work at p problems per hour.

Say there are x problems altogether. It takes me x/p hours to finish and this equals t

It will take my friend x/(2p-4) hours to finish and this is t-2 hours.

p>10

so

\(\frac{x}{p}=t \qquad and \qquad \frac{x}{2p-4}=t-2\\ so\\ \frac{x}{2p-4}=\frac{x}{p}-2\\ 2=\frac{x}{p}-\frac{x}{2p-4}\\ 2=x(\frac{1}{p}-\frac{1}{2p-4})\\ 2=x(\frac{2p-4}{{p(2p-4)}}-\frac{p}{p(2p-4)})\\ 2=x(\frac{2p-4-p}{{p(2p-4)}})\\ 2=x(\frac{p-4}{{p(2p-4)}})\\ 2*(\frac{{p(2p-4)}}{p-4})=x\\ x=\frac{4p(p-2)}{p-4} \)

I decided to use a graphing program to help me.

so I had to swap the p for an y.

p>10 so y>10

Here is the full graph

https://www.desmos.com/calculator/e7xt74l0mi

Here is the extract

It looks like there is more than one answer.

If p = 12, x=60 and t = 60/12=5 So that is a good possiblilty

If p=20 then x=90 but t = 4.5 which is not an integer so that is not a possiblilty.

So the smallest answer that works appars to be p=12, x=60 and t =5

So there are 60 questions.

I answer 12 an hour so it takes me 5 hours.

My friend answers 20 an hour so it takes hime 3 hours.

So it takes him 2 hours less than me which is how it should be.

**So the smallest and most sensible answer is that there are 60 questions.**

Melody Jul 5, 2018