please help with these questions

[jrhae]

1.The width of a rectangle is 6 meters less than the length. The area is 112 meter2. Find the length and the width of the rectangle.

2.Mickey and Minne want to paint a table. Mickey can do it in 5 hours while Minnie can do it in 3 hours. How long will it take them working together?

 

[emmaiskool242]

1.The width of a rectangle is 6 meters less than the length. The area is 112 meter2. Find the length and the width of the rectangle.


My suggestion would be to draw a picture
need to plug it into a formula, we know that area = L*W and
So you would do it like this 112=(x)(x-6)
Because the length is unknown and you know that the width is length(x)-6 so that
Then you would solve it GOOD LUCK

 

[Denis]

1.The width of a rectangle is 6 meters less than the length. The area is 112 meter2. Find the length and the width of the rectangle.

2.Mickey and Minne want to paint a table. Mickey can do it in 5 hours while Minnie can do it in 3 hours. How long will it take them working together?

1: as Emma says: x(x-6) = 112; so solve x^2 - 6x - 112 = 0

2: in one hour: Mickey does 1/5 of work, Minnie does 1/3 of work
so in one hour 1/5 + 1/3 = 8/15 of work is done: how long for 15/15 ?

 

[mowlick]

1.The width of a rectangle is 6 meters less than the length. The area is 112 meter2. Find the length and the width of the rectangle.

2.Mickey and Minne want to paint a table. Mickey can do it in 5 hours while Minnie can do it in 3 hours. How long will it take them working together?

(i)

The rectangle is x metres long and (x - 6) metres wide.

Therefore the area of the table = x(x - 6)

The area is given as 112 metres^2

therefore

x(x - 6) = 112 =

x^2 - 6x = 112

therefore

x^2 -6x -112 = 0 =

(x + 8)(x - 14) = 0

therefore

x + 8 = 0, therefore x = -8

and

x - 14 = 0 therefore x = 14

the only time you will encounter a negative length is in Star Trek so we can ignore x = -8

therefore x = 14

therefore the length of the rectangle is 14 metres and the width is 14 - 6 = 8



(2)

Mickey takes 5 hours to finish the job so will have done 1/5 of the work in 1 hour

Minnie takes 3 hours so will have done 1/3 of the job in 1 hour

1/5 + 1/3 =

(5 x 1 + 3 x 1)/ (3 x 5) =

(5 + 3)/ 15 =

8/15

therefore 8/15 of the job will be done in an hour

1 divided by 8/15 =

15/15 divided by 8/15 =

15/15 x 15/8 =

15/8

Therefore the job takes 15/8 hours = 1.875 hours = 1 hour 52 minutes 30 seconds




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