help on this word problem

Dominique can ice cupcakes twice as fast as Houston. When they work together, Dominique and Houston can ice a large order of cupcakes in 5 hours. How many hours would it take Houston to ice them by himself?

1

4

thirteen-halves

fifteen-halves

Question

help on this word problem

Dominique can ice cupcakes twice as fast as Houston. When they work together, Dominique and Houston can ice a large order of cupcakes in 5 hours. How many hours would it take Houston to ice them by himself?

1

4

thirteen-halves

fifteen-halves

tkhunny · Answer

Please write down names for the two missing rates.

anonymous · Answer

how would i write this in a equation to find the answer??

anonymous · Answer

5=2x+x ??? im really bad at these

mertsj · Answer

Dominique takes x hours to do the job
Houston takes 2x hours to do the job
In 1 hour Dominique gets 1/x of the job done
In 1 hour Houston gets 1/(2x) of the job done
Since it takes them 5 hours to get the job done, in one hour they do 1/5 of the job.
So the part Houston does in 1 hour plus the part Dominique does in 1 hour = 1/5

mertsj · Answer

$$\frac{1}{x}+\frac{1}{2x}=\frac{1}{5}$$

jdoe0001 · Answer

Dominique takes x hours to do the job    <---- wouldn't that give how long Dominique would take if she were to do it by herself?

mertsj · Answer

yes

jdoe0001 · Answer

seems to me none of the choices match, or there's a typo somewhere

anonymous · Answer

no thats exactly how it says :/

jdoe0001 · Answer

hmmm

mertsj · Answer

$$\frac{1}{x}\times10x+\frac{1}{2x}\times10x=\frac{1}{5}\times10x$$
10+5=2x
$$15=2x$$
\[x=7.5 hours for Dominique to do the job by herself
2x=15 hours for Houston to do the job by himself

jdoe0001 · Answer

yeap... 15 is about right... but is none of the choices, for Houston 

I had one of these yesterday, and the choices matched the other gal's rate as well

jdoe0001 · Answer

so the choices do fit, Domique's rate, but not Houston's

mertsj · Answer

I'm guessing some graduate student got the x and 2x mixed up because of the way the problem is worded.

anonymous · Answer

so the answer is 15/2

mertsj · Answer

That's the closest answer.  That is actually Dominique's time but Houston's is not a choice.  So is this a test or what?

anonymous · Answer

yes for my virtual school. ty

mertsj · Answer

Well choose 15/2 and see if it is right.

mertsj · Answer

Was it right?

anonymous · Answer

i have 2 more question till i've finished the test but i will message u the answer :)

mertsj · Answer

ok.  ty

anonymous · Answer

yes it was 15/2

mertsj · Answer

ty