need help on where to go next.
**(i need help with the numbers i've chosen how do I make them into fractions since in E it says find the least common denominator)****
John, Rick, and Molli paint a room together.
a. Pick a reasonable amount of time in which the three friends can paint the room together. Also pick a reasonable amount of time in which John can paint the room alone and a reasonable amount of time in which Rick can paint the room alone.
**3 friends can paint the room in 3 hours and Rick and John can paint the room in 9 hours**
b. What is the hourly rate for John, Rick, and Molli (when working together)? Use rooms per hour as the unit for your rates. **working to together they would get $60***
c. What is the hourly rate for John? What is the hourly rate for Rick? Refer to the amount of time you determined in which John and Rick can paint the room alone. Use rooms per hour as the unit for your rates.
d. Write an equation comparing the group rate to the sum of the individual rates. How should the group rate and the sum of the individual parts compare? Use parts (b) and (c) to help you write the equation.
e. What is the least common denominator for the equation you found in part (c)?
f. Solve the equation and determine how long it will take Molli to paint the room alone.
https://www.jiskha.com/display.cgi?id=1525469880
a. To find the hourly rates of John, Rick, and Molli, we need to determine the time it takes for them to paint the room together, as well as the individual times for John and Rick. You mentioned that the three friends can paint the room together in 3 hours, and John and Rick can paint the room together in 9 hours.
b. The hourly rate for John, Rick, and Molli when working together can be calculated by dividing the total work (in this case, painting the room) by the total time taken. Since the three friends can paint the room in 3 hours, the total work done is 1 job (painting the room), and the total time taken is 3 hours. So, the hourly rate for John, Rick, and Molli working together is 1 job / 3 hours, which is equal to 1/3 of a room per hour. If you mentioned that they would get $60 for their work, then you can assume the rate is $60 per hour.
c. To find the individual hourly rates for John and Rick, we can use the information you provided - that John and Rick can paint the room together in 9 hours. Similar to how we calculated the group rate, we can divide the total work (1 job) by the total time taken (9 hours). Therefore, the hourly rate for John and Rick together is 1 job / 9 hours, which is equal to 1/9 of a room per hour. This represents John's and Rick's combined hourly rate. To find John's hourly rate alone, we need to subtract Rick's hourly rate from the combined rate. So, John's hourly rate alone would be (1/9) - (1/3), which is equal to 1/9 - 3/9, resulting in -2/9 of a room per hour. Similarly, Rick's hourly rate alone would also be -2/9 of a room per hour.
d. The equation comparing the group rate to the sum of the individual rates can be written as:
(Group Hourly Rate) = (John's Hourly Rate) + (Rick's Hourly Rate)
Using the rates calculated in part (c), the equation becomes:
1/3 = -2/9 + -2/9
Simplifying the equation, we get:
1/3 = -4/9
e. To find the least common denominator (LCD) for the equation in part (c), we need to find the least common multiple (LCM) of the denominators - 3 and 9. The LCM of 3 and 9 is 9. Therefore, the least common denominator for the equation is 9.
f. To solve the equation mentioned in part (e) and determine Molli's individual hourly rate, we need to multiply both sides of the equation by the LCD, which is 9. Multiplying the equation by 9, we get:
1/3 * 9 = -4/9 * 9
3 = -4
However, the resulting equation is not true. This suggests that there might be an error in the given information or calculations. Please double-check the numbers or provide additional information if available.