Question

I'll give you a medal and be a fan if you HELP PLEASE

1. The pump used to fill the water tank on a fire truck takes 40 minutes to fill the tank. If the pump sending water to the hose is on, it takes 60 minutes to fill the tank. If the pump filling the water tank is off, how long does the pump sending water to the hose take to empty the tank?
A. 120 minutes
B. 60 minutes
C. 30 minutes
D. 24 minutes

2. Annmarie can plow a field in 240 minutes. Gladys can plow a field 80 minutes faster. If they work together, how many minutes does it take them to plow the field?
A. 96 minutes
B. 160 minutes
C. 400 minutes
D. 480 minutes

3.Brody can fill a bowl with candy in 3 minutes. While Brody fills the bowl, Hudson takes the candy out of the bowl. With Hudson taking candy out of the bowl, it takes 5 minutes for Brody to fill the bowl.
Which of the following can be used to determine the amount of time it takes for Hudson to empty the bowl if Perry does not add candy?
A. 1 over 3 minus 1 over x equals 1 over 5
B. 1 over 3 minus 1 over 5 equals 1 over x
C. 1 over 5 minus 1 over x equals 1 over 3
D. 1 over 3 minus 1 over x equals x over 5

4. Leanne can clean a fish tank in 30 minutes. Karl can clean a fish tank in 20 minutes. If they work together, how many minutes does it take them to clean a fish tank?
A. 6 minutes
B.10 minutes
C. 12 minutes
D. 50 minutes

5.Genna can build a cabinet in 4 hours. Claude can build a cabinet in only 3 hours.

Which of the following can be used to determine the amount of time it would take for Genna and Claude to build a cabinet together?

A. 1 over 4 plus 1 over x equals 1 over 3
B. 1 over 4 plus 1 over 3 equals 1 over x
C. 1 over x plus 1 over 3 equals 1 over 4
D. 1 over 3 plus 1 over 4 equals x over 7

Answer 1

@ganeshie8

Answer 2

@iGreen

Answer 3

@Michele_Laino

Answer 4

@TheSmartOne

Answer 5

Question 5)
the working rate of Genna is W/4, the working rate of Claude is W/3, where W is the work to do.
When Gwenna and Claude work together, then the working rate is:
W/4 + W/3
so we can write:
\[\Large \left( {\frac{W}{4} + \frac{W}{3}} \right)t = W\]
where t is time needed to Genna and Claude to do the work W
Please solve that equation for T, what do you get?

Answer 6

oops.. for t, what do you get?

Answer 7

3 hrs?

Answer 8

hint:
what is:
\[\frac{1}{4} + \frac{1}{3} = ...?\]

Answer 9

\[\frac{ 7 }{ 12 }\]

Answer 10

ok! so, from preceding equation, we can write:
\[\frac{{7W}}{{12}}t = W\]
or:
\[\frac{7}{{12}}t = 1\]

Answer 11

ok

Answer 12

namely:
\[t = \frac{{12}}{7}\]

Answer 13

so the answer is D then?

Answer 14

yes!

Answer 15

Thanks ! can you help with the others
?

Answer 16

ok!
Question 4)

Answer 17

the working rate of Leanne is W/30, where the working rate of Karl is W/20, where as usual, W is the work to do.
So when Leanne and Karl work together the working rate is:
W/30+ W/20, and we can write:
\[\Large \left( {\frac{W}{{30}} + \frac{W}{{20}}} \right)t = W\]
where t is time neeeded to Leanne and Karl to finish the work W.
Please solve for t

Answer 18

oops...whereas the working rate of Karl

Answer 19

as before, we can write:
\[\Large \left( {\frac{1}{{30}} + \frac{1}{{20}}} \right)t = 1\]

Answer 20

what is t?

Answer 21

\[\frac{ 5 }{ 15 } ?\]

Answer 22

we have:
\[\frac{1}{{30}} + \frac{1}{{20}} = \frac{{2 + 3}}{{60}} = ...?\]

Answer 23

i entered the wrong thing my bad!

Answer 24

\[\frac{ 1 }{ 12 }\]

Answer 25

ok!
So we have:
\[\frac{t}{{12}} = 1\]

Answer 26

and therefore:
\[t = 12 \times 1 = ...?\]

Answer 27

12?

Answer 28

that's right!

Answer 29

it is 12 minutes

Answer 30

Ok Thanks!

Answer 31

Have time for another one?

Answer 32

yes!

Answer 33

question 3)

Answer 34

ok

Answer 35

I'm pondering....

Answer 36

the working rate of Brody is:
W/3, when he works alone
whereas the working rate of Brody is W/5, when Brody and Hudson work together
W is the work to be done
Now the working rate of Hudson is:
W/x, where x is the unknown quantity. So, we can write:
\[\Large \frac{W}{3} - \frac{W}{x} = \frac{W}{5}\]
or:
\[\Large \frac{1}{3} - \frac{1}{x} = \frac{1}{5}\]
so, what is the right option?

Answer 37

hint:
\[\Large \frac{1}{x} = \frac{1}{3} - \frac{1}{5}\]

Answer 38

@amielli

Answer 39

2/15

Answer 40

yes! What is the right option?

Answer 41

D?

Answer 42

I think that option D is wrong

Answer 43

please look at this equation:
\[\Large \frac{1}{3} - \frac{1}{x} = \frac{1}{5}\]
do you recognize to which option corresponds to?

Answer 44

yes that would be A

Answer 45

yes! correct!

Answer 46

I dont get it though

Answer 47

since Brody is filling the bowl, he is adding candies to that bowl.
Hudson is subtracting candies to that bowl.
Here is why I used the minus sign in the subsequent equation:
\[\large \frac{W}{3} - \frac{W}{x} = \frac{W}{5}\]

Answer 48

now, is it clear?

Answer 49

Oh yes I do

Answer 50

Thanks

Answer 51

ok!

Answer 52

question 2)

Answer 53

here we can write:
working rate of Annmarie is W/240, whereas the working rate of Gladies is W/80.
Now when Annmarie and Gladies work together, the working rate is:
W/240 + W/80.
As usual W is the work to be done.
So we can write:
\[\Large \left( {\frac{W}{{240}} + \frac{W}{{80}}} \right)t = W\]
or:
\[\Large \left( {\frac{1}{{240}} + \frac{1}{{80}}} \right)t = 1\]
Please solve for t

Answer 54

hint:
\[\Large \frac{1}{{240}} + \frac{1}{{80}} = \frac{{1 + 3}}{{240}} = ...?\]

Answer 55

please wait a moment, I think to have made an error

Answer 56

ok

Answer 57

the working rate of Gladies is:
\[\Large \frac{W}{{240 - 80}} = \frac{W}{{160}}\]

Answer 58

so the right equation is:
\[\Large \left( {\frac{W}{{240}} + \frac{W}{{240 - 80}}} \right)t = W\]

Answer 59

or:
\[\Large \left( {\frac{1}{{240}} + \frac{1}{{160}}} \right)t = 1\]

Answer 60

please solve for t, keep in mind that:
\[\Large \frac{1}{{240}} + \frac{1}{{160}} = \frac{{2 + 3}}{{480}} = \frac{5}{{480}}\]

Answer 61

after a substitution, we have:
\[\Large \frac{5}{{480}}t = 1\]
what is t?

Answer 62

just simplify it?

Answer 63

hint:
\[\Large t = \frac{{480}}{5} = ...?\]

Answer 64

96

Answer 65

I get that one

Answer 66

So the last one

Answer 67

ok! question 1)

Answer 68

this question is similar to the question of candies, namely question 3).
So the rate of working for the pump is W/40, when the pump works alone
the working rate of the firehose is W/x, where x is the unknown quantity
and
W/60 is the working rate of the pump, when the pump and the firehose work together.
So we can write:
\[\Large \frac{W}{{40}} - \frac{W}{x} = \frac{W}{{60}}\]
or:
\[\Large \frac{1}{{40}} - \frac{1}{x} = \frac{1}{{60}}\]

Answer 69

so the answer is 60?

Answer 70

no, since we have to compute the value of x

Answer 71

hint:
\[\Large \frac{1}{x} = \frac{1}{{40}} - \frac{1}{{60}} = \frac{{3 - 2}}{{120}} = ...\]

Answer 72

please continue my computation

Answer 73

1/120

Answer 74

ok! so we have:
\[\Large x = \frac{{120}}{1} = ...{\text{minutes}}\]

Answer 75

thanks very much I got 80%

Answer 76

number 5 was wrong

Answer 77

are you sure?

Answer 78

I'm very sorry, the correct answer is option B.
Sorry again

Answer 79

That is totally fine

Answer 80

Thanks!

Answer 81

since we can write this:
\[\Large \left( {\frac{W}{4} + \frac{W}{3}} \right)t = W\]
and then:
\[\Large \frac{1}{4} + \frac{1}{3} = \frac{1}{t}\]
Sorry again

Answer 82

thanks for your comprehension!

Answer 83

Thanks for helping me