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Tanya [424]
3 years ago
13

It takes Alexandra 2 hours and 44 minutes to cut the grass. Austin needs 3 hours and 14 minutes to cut the grass. If they work t

ogether, how long will it take them to cut the grass?
Please show work! :)
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
6 0
For problems such as this, it can be handy to remember that
.. 1/(1/a +1/b) = ab/(a +b)

The time required to do a job is the inverse of the rate at which the job is done. Rates are added when people work together (in math problems, not in real life).

(2:44)*(3:14)/(2:44 +3:14) = 1:28:52.3

___
2:44 = 41/15 hours = 82/30 hours
3:14 = 97/30 hours
Using the formula above, we have a "working together" time of
.. (82/30)*(97/30)/(82/30 +97/30) = 82*97/(30*179) = 3977/2685 . . . hours
.. = 1 hour 28 156/179 minutes
.. = 1 hour 28 minutes 52 52/179 seconds

___
Learn to use the fraction functions on your calculator. They can be very helpful.
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How many solutions does the equation y=3x have?
Butoxors [25]

Answer:

1 solution

Step-by-step explanation:

If you were to graph this line it would be a straight line so there is 1 solution.

y=3x

x=y/3

7 0
2 years ago
Select all points that are on the line through 0,5
Rus_ich [418]

Answer:

Options (1), (3), and (4)

Step-by-step explanation:

Since, slope of a line passing through two points (x_1,y_1) and (x_2,y_2) is given by,

m = \frac{y_2-y_1}{x_2-x_1}

Therefore, slope of a line passing through (0, 5) and (2, 8) will be,

m = \frac{8-5}{2-0} = 1.5

Equation of line passing through (x', y') and slope 'm' is,

y - y' = m(x - x')

Therefore, equation of a line passing through (0, 5) and slope = 1.5,

y - 5 = 1.5(x - 0)

y = 1.5x + 5

Since, all the points which lie on this line will satisfy this equation.

For (4, 11),

11 = 1.5(4) + 5

11 = 11

Point (4, 11) lies on this line.

Point (5, 10)

10 = 1.5(5) + 5

10 = 7.5 + 5

10 = 12.5

But 10 ≠ 12.5

Therefore, (5, 10) doesn't line on the line.

Point (6, 14)

14 = 1.5(6) + 5

14 = 14

True.

Therefore, (6, 14) lies on the line.

Point (30, 50)

50 = 1.5(30) + 5

50 = 50

True.

Therefore, (30, 50) lies on the line.

Point (40, 60)

60 = 1.5(40) + 5

60 = 65

But 60 ≠ 65

Therefore, (40, 60) doesn't lie on the line.

Options (1), (3) and (4) and the correct options.

3 0
2 years ago
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Gran knitted many wash clothes for the school fundraiser. She sold 42 cloths at the sale. There were 11 washcloths left after th
defon

Answer:

53

Step-by-step explanation:

c=42+11

c=53

5 0
3 years ago
Someone help me solve this and could you explain why too?
yulyashka [42]

Answer:

3.5

Step-by-step explanation:

Well its easiest to just plug in the answers and see like 2 times 3.5 is 7.

Another way is saying 7 divided by 2 is 3.5

then u check to make sure its the same for all the numbers.

Which it is because 21 divided by 6 is also 3.5 :)

5 0
3 years ago
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