Please help me ASAP!!! I HAVE NO IDEA HOW TO DO THIS!!!!
John, Rick, and Molli can paint a room working together in 6 hours. Alone, John can paint the room in
12 hours. If Rick works alone, he can paint the room in 15 hours. Write an equation comparing the
group rate to the sum of the individual rates. Then find how long it will take Molli to paint the room if
working alone.
a. What is the equation?
b. What is the lowest common denominator for the equation in part a?
c. Show all work below in solving equation from part a.
John's rate = 1/12
Rick's rate = 1/15
Molly's rate = 1/x
cominged rate = 1/12 + 1/15 + 1/x
= (5x + 4x + 60)/60x
so 1 / ( (5x + 4x + 60)/60x ) = 6
60x/(9x + 60) = 6
54x + 360 = 60x
x = 60
Molly's cand do the room in 60 hours by herself
check: 1/12 + 1/15 + 1/60 = 1/6 , as needed
THANK YOU SO MUCH!!!!!
a. 1/T1 + 1/T2 + 1/T3 = 1/6,
1/12 + 1/15 + 1/T3 = 1/6.
b. LCD = 60.
c. 1/12 + 1/15 + 1/T3 = 1/6,
1/T3 = 1/6 - 1/12 - 1/15,
1/T3 = 10/60 - 5/60 - 4/60 = 1/60,
T3 = 60 hrs. = Molli's time.
Thank you!:-)
a. The equation comparing the group rate to the sum of the individual rates is:
1/6 = 1/12 + 1/15 + 1/x, where x represents the time taken by Molli alone.
b. To find the lowest common denominator for this equation, you need to determine the least common multiple (LCM) of 12 and 15. The LCM of 12 and 15 is 60.
c. To solve the equation, let's first convert the individual rates' fractions to have a denominator of 60:
1/6 = 5/60 + 4/60 + 1/60
1/6 = 10/60 + 8/60 + 1/60
Next, combine the fractions:
1/6 = (10 + 8 + 1)/60
1/6 = 19/60
To isolate Molli's rate, subtract the combined rates of John and Rick from the group rate:
19/60 - (10/60 + 8/60) = 19/60 - 18/60 = 1/60
This means that Molli can paint the room alone in 60 hours.
So, Molli takes 60 hours to paint the room by herself.
a. To write the equation comparing the group rate to the sum of the individual rates, we can use the concept of "work done per unit of time".
Let's denote the rate at which John, Rick, and Molli can paint the room together as JRM (Group rate). The rate at which John can paint the room alone is J, and the rate at which Rick can paint the room alone is R. We want to find the rate at which Molli can paint the room alone, denoted as M.
The equation comparing the group rate to the sum of the individual rates is:
JRM = J + R + M
b. To find the lowest common denominator for the equation in part a, we need to consider the fractions involved in the rates. Here, all the rates have a denominator of 1 since they represent hours per room. Therefore, the lowest common denominator is also 1.
c. To solve the equation from part a, we can use the given information.
Given:
JRM = J + R + M
JRM = 1/12 + 1/15 + M
To combine the fractions on the right side, we need a common denominator. The common denominator is the lowest common denominator, which is 1.
JRM = (15/180) + (12/180) + M
JRM = (27/180) + M
Now we can see that JRM is the reciprocal of 6. So, we can rewrite the equation as:
1/6 = (27/180) + M
To solve for M, we need to isolate it. Subtracting (27/180) from both sides, we get:
1/6 - (27/180) = M
Simplifying the left side of the equation:
30/180 - 27/180 = M
3/180 = M
The final step is to simplify the fraction:
M = 1/60
Therefore, it will take Molli 1/60 of an hour to paint the room alone.