Shelby can paint a room in 4 hours. Zoe can paint the same room in 7 hours. How long will it take them to paint the room if they work together? If they start 9:30a.m., and want to see a movie that is playing 45 minutes from their house and starting 12:00 p.m., will they make it on time? If they can make it, how early are they? If they will be late, how late will they be?
Please let me know if I am correct.
First I took the average of 4 and 7 and got 5.5 hours. So they can both paint the room in 5.5 hours.
Next, If they start at 9:30 they will finish at 3:00
Next if they have to leave 45 minutes early to get to a 12:00 show, they should leave at 11:15.
Next, therefore, they will be 3:45 minutes late for the 12:00 show.
You cant trust the average always.
I assume you are using a rate equation,
amount=rate*time
Consider in 28 hours, shelby can paint 7, and Zoe can paint 4. So the combined rate = (7+4 rooms)/28 hrs= 11/28 rooms/hr
Now the time to paint one room
amount= rate*time
time= amount/rate= 1room/(11/28 room/hr)
time= 1*28/11 hrs= 2.54hrs= 2hrs 33min
If they start at 9:30, then they finish about three min after noon. Check my thinking and calculations.
Now on your thinking... Using the average 5.5hrs per room, but BOTH are working, that is the average for each, so time for both together would be 5.5/2= 2.75hrs, which is not 28/11 hrs (2.545hrs). SO don't use the average, throw away that thinking, it wont work.
Thank you soooooooo much, you are a great teacher! I truly understand!
To find the amount of time it takes Shelby and Zoe to paint the room together, you can use the formula:
(1/4 + 1/7)^-1
The sum of the rates at which Shelby and Zoe paint is 1/4 + 1/7. Inverting this sum gives you the combined time it takes for them to complete the job.
To make the calculation easier, you can find a common denominator for 4 and 7, which is 28. The equation becomes:
(7/28 + 4/28)^-1
Simplifying the equation, you get:
(11/28)^-1
Inverting this fraction gives:
28/11
Therefore, it will take Shelby and Zoe approximately 2.54 hours, or 2 hours and 32 minutes, to paint the room together.
Next, let's calculate the time they need to leave to make it to the movie on time. They want to start the movie at 12:00 p.m. and it takes them 45 minutes to get there. So, they need to leave their house at:
12:00 p.m. - 0 hours and 45 minutes = 11:15 a.m.
Therefore, if they start painting at 9:30 a.m., they will have enough time to make it to the movie on time.
Finally, let's calculate the time difference between when they would finish painting and when they need to leave. They finish painting at 3:00 p.m., and they need to leave at 11:15 a.m., so the difference is:
3:00 p.m. - 11:15 a.m. = 3 hours and 45 minutes.
Therefore, they are 3 hours and 45 minutes early for the movie, not late.
You are almost correct with your calculations, but there are a couple of errors.
To find how long it will take Shelby and Zoe to paint the room together, you need to find their combined work rate. The formula for this is:
(1/time taken by Shelby) + (1/time taken by Zoe) = (1/combined time)
Since Shelby can paint the room in 4 hours and Zoe can paint the same room in 7 hours, the equation becomes:
(1/4) + (1/7) = (1/combined time)
Simplifying this equation gives:
7/28 + 4/28 = 1/combined time
11/28 = 1/combined time
To find the reciprocal of 11/28, you flip the fraction, giving 28/11. Therefore, the combined time is 28/11 hours, which is approximately 2.54 hours or 2 hours and 32 minutes. So, it will take Shelby and Zoe about 2 hours and 32 minutes to paint the room together.
Now, let's move on to the second part of the question about the movie.
If they start painting at 9:30 a.m. and finish at 3:00 p.m., the total time they spend painting is 5 hours and 30 minutes (since there are 60 minutes in an hour).
To determine if they can make it to the movie at 12:00 p.m., we need to calculate how much time they have left after finishing painting.
If they finish at 3:00 p.m., subtract 5 hours and 30 minutes from 3:00 p.m. to get the remaining time.
3:00 p.m. - 5 hours and 30 minutes = 9:30 a.m.
So, they finish painting at 9:30 a.m., which is the same time they started. Therefore, they will have enough time to get to the movie at 12:00 p.m. since they do not need to leave early.
If they had to leave 45 minutes early, as mentioned in the question, they would subtract 45 minutes from the starting time:
9:30 a.m. - 45 minutes = 8:45 a.m.
As the movie starts at 12:00 p.m., they would have 3 hours and 15 minutes to get ready and travel from their house to the movie theater.
So, they are actually 3 hours and 15 minutes early for the movie.
In summary:
- Shelby and Zoe will take approximately 2 hours and 32 minutes to paint the room together.
- They will finish painting at 9:30 a.m., which leaves them with enough time to get to the movie at 12:00 p.m., without needing to leave early.
- If they had to leave 45 minutes early, they would be 3 hours and 15 minutes early for the movie.