If it takes 11/2 hours to fill an aquarium and 11/3 hours to drain it, how long will it take to empty the tank and refill it

Question

e.mccormick · Answer

OK.  What did you have trouble with on this?

anonymous · Answer

i added 11/3 and 11/2 which gave me 55/6

anonymous · Answer

how do i convert it to hour

e.mccormick · Answer

It is still hours.  No conversion.  55/6 hours.

e.mccormick · Answer

They gave you two number in hours so you got an answer in hours.  Now, if they gave you one in hours and one in minutes, you would need to convert first to they were both in the same units before adding.  But, because they gave it to you all in hours, no problems.

anonymous · Answer

the options are a)2 hours and 3 min
b) 2 hours and 40 mins
c) 2 hours and 45 mins
d) 2 hours and 50 mins
e) 2 hours and 55 mins

anonymous · Answer

i mean a) 2 hours and 30 mins

e.mccormick · Answer

AAAH!  Ok.Is that 11/2 and 11/3 or is it 1 and 1/2, and 1 and 1/3?

anonymous · Answer

it's 11/2 and 11/3

mertsj · Answer

Perhaps it sis
$$1\frac{1}{2}$$

e.mccormick · Answer

Yah, which is why I was asking because that would make it add to one of the answers.

mertsj · Answer

Exactly.  If it is 
$$\frac{11}{2}$$
the answer is not there.

e.mccormick · Answer

$$1\frac{1}{2}+1\frac{1}{3}=?$$

e.mccormick · Answer

If you look at this as 1 hour plus half an hour plus one hour plus a third of an hour, it becomes two hours and?  Half and hour and a third of an hour are how many minutes?

anonymous · Answer

i have one more question

anonymous · Answer

If 5/7 of the lawn is cut in 35 mins, then how much more time, in minutes, will it take to finish the job

e.mccormick · Answer

OK.  So This is a ratio problem with a twist.  Do you know how to set those up?

anonymous · Answer

no

e.mccormick · Answer

OK.  The big thing here is you have 5/7 of a lawn but you want a whole lawn.  A whole lawn is one lawn.  So, 5/7 + x = 1.  What is x?  Lets start there.

anonymous · Answer

ok

e.mccormick · Answer

So, can you solve that?  What added to 5/7 makes for 1, or another way to say that is:$$\frac{5}{7}+\frac{?}{?}=\frac{7}{7}$$

anonymous · Answer

7/7- 5/7

e.mccormick · Answer

Yes.  Which is?

anonymous · Answer

2/7

e.mccormick · Answer

OK.  Now you know how much of the lawn is the rest of the lawn.  So lets use L for lawn.$$\frac{5}{7}L=35$$and what you want is $$\frac{2}{5}L=Answer$$  There are a couple ways to solve it at that point.  Can you think of one that might work?

e.mccormick · Answer

Sorry.  Second is supose to be 2/7L  Oops!

anonymous · Answer

no

e.mccormick · Answer

OK.  Lets start by finding what those 5/7ths are.  So you know you have 35, and that represents 5 of something broken into 7 parts.  To me, that means 5 of something is somehow related to 35.  So what do you get if you divide 35 by 5?

e.mccormick · Answer

Mathematically this is:

$$\frac{5}{7}L*\frac{1}{5}=\frac{35}{1}*\frac{1}{5}$$

e.mccormick · Answer

Now, if you simplify that, what would you get on the right and left.  You can ignore the L for doing the simplification and just focus on the fractions.

e.mccormick · Answer

Well, it says you are offline.  Once you know that simolified form above, you will have 1/7th L = something.  You want 2/7ths, so multiply the something by 2 and you have the answer.

anonymous · Answer

I got it. thank you very much.