Question

MEDAL!!!!! If it takes Wilbur 3 hours to rake the leaves in a neighbors’ backyard, and it takes his friend, Orville 6 hours to rake the same amount of leaves, how long would it take Wilbur and Orville to rake the leaves in a neighbors’ backyard together?

Answer 1

The equation is 1 over 3 + 1 over 6 = 1 over x

I multiplied each part by 6x and wound up getting 2x + x = 6.

How do I solve from here?

Answer 2

So you have 1/3 + 1/6 = 1/x

Answer 3

Would the common multiple be 6x?

Answer 4

Next RULE: combine all numbers on one side

Answer 5

and the variable on the other side

Answer 6

So first, leave the variable alone and combine "1/3 + 1/6" on the left side

Answer 7

How do I do that?

Answer 8

"1/3 + 1/6" =

"2/6 + 1/6"

Answer 9

=3/6

Answer 10

=1/2

Answer 11

Now we have 1/2 = 1/x

Answer 12

Next RULE: solve for x

Answer 13

To do so, we would normally need to isolate x by multiplying or dividing. Here, we know x by just looking at the equation above

Answer 14

Solve from the 1/2, you mean?

Answer 15

Hint:
1/___ =1/____
1/2=1/2
1/3=1/3
1/4=1/4
1/5=1/5

Answer 16

1/2 = 1/x
1/2 = 1/2
x=2

Answer 17

Oh, I see, because then 2 makes each of the fractions equal zero?

Answer 18

Lets simplify this:

The RULE we use to solve this:

to isolate a variable, subtract, add, multiply and divide to get numbers on one side and variables on the other side

Answer 19

Lets apply this rule

Answer 20

So you have 1/3 + 1/6 = 1/x

Answer 21

Yes, okay..

Answer 22

combine "1/3 + 1/6" on the left side

Answer 23

2/6 + 1/6 on the left side

Answer 24

=3/6 on the left side
=1/2 on the left side

Answer 25

We have 1/2 = 1/x. Now, lets isolate the variable x

Answer 26

to do so, multiply each side by x

Answer 27

giving us x/2 = 1

Answer 28

Ok, so in order for the two sides to equal the same, the right has to be a 1/2 too, no?

Answer 29

next, multiply each side by 2

Answer 30

that is one way to look at it-but it is a shortcut so I am re-doing the problem...disregard my prior explanation

Answer 31

so multiplying each side by 2, we get x=2

Answer 32

Just use the rule "to isolate a variable, subtract, add, multiply and divide to get numbers on one side and variables on the other side"

Answer 33

Ohhhh, okay, I understand it better now; thanks:)

Answer 34

One question though, how did the 1/3 turn into 2/6 in the beginning?

Answer 35

multiply 1/3 x 2/2

Answer 36

An in-person drawing would work better here...I will draw the explanation later if you do not understand (gotta go now unfortunately)

Answer 37

to make the LCD for the left side 6

Answer 38

That's okay, but why was 2/2 multiplied by the 1/3 and not the 1/6?