Joon and Sae can clean the house in 6 hours if they work together. Joon can clean the house alone in 5 hours more than the time Sae take in cleaning the same house.How long does it takes Joon to clean the house alone?How about Sae?
GIVEN:
REPRESENTATION:
EQUATION:
SOLUTION:
ANSWER:
Answers
Answer:
Let Joon take x hours.
Sae will take x - 5 hours.
In 1 hour Joon can clean 1/x part.
In 1 hour Sae can clean 1/x-5
In 1 hour both can clean = 1/x + 1/(x-5)
= (2x - 5)/(x² - 5x)
which is 1/6 th of the house since they can complete in 6 hours.
(2x - 5)6 = (x² - 5x)
⇒ 12 x - 30 = x² - 5x
⇒ x² - 17 x + 30 = 0
⇒ (x - 15)(x - 2) = 0
x has to be 15 hours logically..
ANS : 15 , 10
Step-by-step explanation:
Let t equal the amount of hours it takes each maid to finish.
First Maid: t/6
Second maid: t/5
Total hours: 1
t/6+t/5=1
5 and 6 both go into 30.
5 goes into thirty 6 times. So now we have 6t
6 goes into thirty 5 times. So now we have 5t
Since 30 is the greatest common factor the 1 now becomes 30.
Our equation now looks like: 5t+6t=30
Add 5t and 6t together and you will get 11t.
11t=30
t=30/11
t= 2.72 hours or 2 hours 44 minutes.