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How long does it take Natsumi to clean up after she is done?

TABLE:.

AREA TIME
30. 2
45. 2.75
60. 3.5

How long does it take Natsumi to clean up after she is done? TABLE:. AREA TIME 30. 2 45. 2.75 60. 3.5-example-1
User Nullqwerty
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2 Answers

3 votes

Explanation:

User Priyanka Mishra
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4 votes

Answer:

0.5 hours

Explanation:

Let the total time to paint and clean = y

and x is the area Natsumi paints

As she paints with a constant speed, so, there is a linear variation between x and y and then she takes a constant a mount to clean

So, the equation which describe this situation is ⇒ y = ax + b

Where a = hours/area and b is a constant a mount to clean.

Using the given table:

at x = 30 m² ⇒ y = 2 hours ⇒ 2 = 30 a + b ⇒ (1)

at x = 45 m² ⇒ y = 2.75 hours ⇒ 2.75 = 45 a + b ⇒(2)

solve (1) and (2) to find a and b

from (1) ⇒ b = 2 - 30a ⇒ (3)

Substitution with (3) at (2)

2.75 = 45a + 2 - 30a

Solve for a:

2.75 - 2 = 45a - 30a

0.75 = 15a

a = 0.75/15 = 0.05 hours/m²

b = 2 - 30a = 2 - 30*0.05 = 0.5 hours

Check the results using the third raw:

at x = 60

∴ y = 0.05 * 60 + 0.5 = 3.5 hours (correct as in table)

So, the time taken to clean up after she is done = 0.5 hours

User Andy Bowskill
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7.5k points