Question

if it takes adis 5 minutes to eat a large pizza and 10 minutes for ray to eat a large pizza/ how long will it take ray and adis to eat it together?

1/5+1/10=1/x each fraction represents the amount of pizza ate per minute. the time it would take both of them is represented by 1/x

Answer 1

\[\frac{5\times 10}{5+10}\]

Answer 2

ok im with you

Answer 3

that is the answer

Answer 4

wait...but

Answer 5

may you show some work please?

Answer 6

ok fine lets do the work and in fact lets replace \(5\) by \(x\) and \(10\) by \(y\) so we never have to do it again

Answer 7

since it take adam \(x\) minutes , he eats \(\frac{1}{x}\) of the apple in one minute
i.e. his rate is \(\frac{1}{x}\)
eve meanwhile eats \(\frac{1}{y}\) of the apple in one minute, i.e. eve's rate is \(\frac{1}{y}\)
their combined rate is what you get if you add, namely
\[\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\] and you want to solve
\[\frac{x+y}{xy}T=1\] for \(T\) the "one" because they are going to eat one apple

Answer 8

solve in one step
\[T=\frac{xy}{x+y}\] a very general result
so when you see
takes 5 minutes for adis and takes 10 minute for ray, they will eat the whole thing in
\[\frac{5\times 10}{5+10}\] minutes

Answer 9

thank you guru.

Answer 10

lol you are welcome, hope the method and steps are clear
you can also do it from scratch each time, but it seems silly
impress your teacher by solving in ten seconds on a quiz
less actually since computing
\[\frac{5\times 10}{5+10}\] take maybe 5 seconds