Bob is packing collector's books into boxes. Each box holds 12 books. Bob packs boxes at the rate of 3 boxes per hour. How many hours will Bob take to pack b boxes?

a. b/3

b. b/4

c. b/12

d. b/15

e. b/36

**i don't really get this :( can you please explain it to me? Thanks!! :)

Question

Bob is packing collector's books into boxes. Each box holds 12 books. Bob packs boxes at the rate of 3 boxes per hour. How many hours will Bob take to pack b boxes?

a.  b/3

b.  b/4

c.  b/12

d.  b/15

e.  b/36

**i don't really get this :( can you please explain it to me? Thanks!! :)

ash2326 · Answer

He packs 3 boxes in an hour, so his packing speed is 3 boxes/hour
Do you get this?

snowfire · Answer

If it helps at all, you can always just substitute b with a number to help understand the concept.

anonymous · Answer

yes :)

snowfire · Answer

Imagine he was trying to pack only one box, what would b be?

anonymous · Answer

ohh so do i just multiply 3 by 12? since 12 books per box? and so in an hour, there are 12x3=36 books being packed?

anonymous · Answer

and since we don't know how long it will take him, is it b/36??

ash2326 · Answer

no books are not required, that information is not required

snowfire · Answer

I don't think the number of books is relevant actually. Correct me if I'm wrong, but the boxes are all we care about here.

anonymous · Answer

ohh okay :( 

could you please explain the next step then? :D

snowfire · Answer

So if we only wanted to pack one box, what is b?

snowfire · Answer

(This isn't a trick question fyi xD)

ash2326 · Answer

So we have to place b boxes, at a speed of 3 boxes/hour. How many hours it'll take?
Imagine this as a distance time problem I have to find time to cover 10 miles with a speed of 2 miles/hour

anonymous · Answer

3b?

ash2326 · Answer

Review again, there is a slight mistake

anonymous · Answer

b/3?

snowfire · Answer

Okay, maybe a proportion will help. If Bob can pack 3 boxes in one hour (which is what the question states) then how long will it take Bob to pack one box?

ash2326 · Answer

yes, do you understand the question now?

anonymous · Answer

i think so... so from there, we multiply the 3 by 12?

anonymous · Answer

is that right?

snowfire · Answer

Ask yourself what each of the numbers is pertaining to. What is the significance of 12 in this problem?

ash2326 · Answer

nope, you have to find the time, which we have got b/3 hours

anonymous · Answer

ohh so the answer is A? b/3?

snowfire · Answer

It is, but explain to me your thought process so that I'm sure you got it for the right reasons.

anonymous · Answer

he packs 3 boxes per hour, but we don't know how long it will take him to pack b boxes... so we need to pack b boxes at the speed of 3 boxes per hour, so that gives b/3. did i understand that correctly?

snowfire · Answer

Well I feel like the wording is a bit vague, but I'll take your word for it ^^ why do you divide b by 3?

anonymous · Answer

3 is the time right?

snowfire · Answer

Replace b with a number as I suggested earlier, and then you might be able to explain better

snowfire · Answer

I feel like that usually helps in any situation

anonymous · Answer

okay, so b=6, b/3=6/3=2, so it will take bob 2 hours to pack 6 boxes?

snowfire · Answer

Yep, and that makes sense doesn't it? 3 boxes per hour, 6 boxes in 2 hours. So if b were 1, he only needs to pack 1 box. Since he can pack 3 in an hour, he only needs to spend 1/3 of that time. Maybe I'm just over-expanding this concept, I'm sure you understand it xD

anonymous · Answer

yes it does. Thanks so much @Snowfire @ash2326 !!! :)

snowfire · Answer

Glad I could help