Question

Suppose the Williams Spring Water Company has two machines that bottle the spring water. Machine X fills the bottles twice as fast as Machine Y. Working together,it takes them 20 min. to fill 450 bottles. How long would it take each machine working alone to fill 450 bottles?

Answer 1

@Euler271

Answer 2

Machine Y fills x bottles per minute
Machine Y fills 20x bottles in 20 minutes
Machine X is twice as fast so:
Machine X fills 2x bottles per minute
Machine X fills 40x bottles in 20 minutes.
Together, in 20 minutes, they fill 450 bottles.
Write and solve the equation.

Answer 3

can you write the Equation for me please? Cause All I see are words... I'm terrible at this sorry.

Answer 4

Did you read the words?

Answer 5

yes I did. Actually let me try it again.

Answer 6

yeup @Mertsj I don't think I set the equation correctly.

Answer 7

How many bottles did Machine Y fill in 20 minutes?

Answer 8

2ox

Answer 9

I think

Answer 10

How many bottle did Machine X fill in 20 minutes?

Answer 11

40x?

Answer 12

Add those two together and what do you get?

Answer 13

60x

Answer 14

And how many bottles does the problem say that is equal to?

Answer 15

450?

Answer 16

So write that equation.

Answer 17

so it would be 60x=450 and you you would solve?

Answer 18

yes. solve that.

Answer 19

7.05?

Answer 20

\[\frac{450}{60}=\frac{45}{6}=\frac{15}{2}=7.5\]

Answer 21

So x is 7.5 and what does x represent?

Answer 22

The amount of bottles?

Answer 23

Be more specific. What number of bottles. Reread what I wrote at the beginning.

Answer 24

The amount of bottles they fills together?

Answer 25

Reread what I wrote at the beginning.

Answer 26

It's either the time or the avg. speed, cause when I keep going back to read what you wrote in the beginning I just get the amount of water bottles.

Answer 27

Machine Y fills x bottles per minute

Answer 28

What does x represent?

Answer 29

the amount of bottles the machine fill per a minute.?

Answer 30

Which machine?

Answer 31

Both of them together?

Answer 32

Machine Y fills x bottles per minute

Answer 33

oh oops lol

Answer 34

So let's see if you can answer this question:
Machine Y can fill ____ bottles each _____

Answer 35

Machine Y can fill 7.5 bottles each minute?

Answer 36

Yes. So we could say that for Machine Y:
7.5(number of minutes)= bottles filled.
Do you see that?

Answer 37

But the answer says Machine X=30 minutes & Machine Y=60 minutes.....

Answer 38

Will you please answer my question?

Answer 39

Yes. So we could say that for Machine Y:
7.5(number of minutes)= bottles filled.
Do you see that?

Answer 40

oh yeah I see it...

Answer 41

So solve that equation for 450 bottles.

Answer 42

\[7.5m=450\]

Answer 43

I got 60~

Answer 44

60 what?

Answer 45

60 minutes

Answer 46

60 minutes for what?

Answer 47

Machine Y

Answer 48

Machine Y to do what?

Answer 49

to fill up bottles

Answer 50

How many bottles?

Answer 51

450?

Answer 52

Yes. So now we know that it takes Machine Y 60 minutes to fill 450 bottles.

Answer 53

Is Machine X faster or slower than Machine Y?

Answer 54

2x faster

Answer 55

So how long would it take Machine X to fill 450 bottles?

Answer 56

30 minutes

Answer 57

So now answer the questions the problem asks.

Answer 58

Machine X=30 minutes
Machine Y=60 minutes

Answer 59

Very good!!

Answer 60

haha Thanks for sticking in there with me!

Answer 61

yw