Answer:
0.5 hours
Step-by-step 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
