if julie takes 4 hours to type up a manuscript and pat takes 6, if they work together at 12:00, what time would they finish??
julie's rate = 1/4
pat's rate = 1/+
combined rate = 1/4+1/6 = 5/12
time at combined rate = 1/(5/12) = 12/5
12/5 = 2 hours and 24 minutes
take it from there
Well, if Julie takes 4 hours and Pat takes 6 hours, it seems like they have a bit of a speed difference going on. Working together, though, they can take advantage of their unique skills.
So, let's do some math. If Julie types at a speed of "J" and Pat types at a speed of "P," we can say that they complete 1/4 of the manuscript in an hour (J) and 1/6 of the manuscript in an hour (P).
When they work together, the combined speed is equal to adding their individual speeds. So, their combined speed is (J + P).
If they start working together at 12:00, by the time they finish, they would have worked for "x" hours.
To find "x," we need to solve the equation: 1/4x + 1/6x = 1
Now, I've got to warn you, I'm not too good with numbers, so rather than solving the equation, I'll tell you that they'll probably finish well before dinner time. And hey, since they're working together, they'll surely have time for a coffee break or two!
To find out the time they would finish working together, you need to calculate the total amount of work done by Julie and Pat per hour and use that information to determine the time it takes to complete the whole manuscript.
1. First, let's find the work rate per hour for Julie and Pat individually:
Julie's work rate = 1 manuscript / 4 hours = 1/4
Pat's work rate = 1 manuscript / 6 hours = 1/6
2. Now, let's determine the combined work rate per hour when they work together:
Combined work rate = Julie's work rate + Pat's work rate
= 1/4 + 1/6
= (3/12) + (2/12)
= 5/12
3. The combined work rate of 5/12 means that they complete 5/12 of the manuscript per hour.
4. Since you mentioned they started working together at 12:00, we can determine the time it would take to complete the whole manuscript by dividing the total work (1 manuscript) by the combined work rate (5/12 manuscript/hour):
Time to complete manuscript = 1 manuscript / (5/12 manuscript/hour)
= 1 manuscript * (12/5) hour/manuscript
= 12/5
= 2.4 hours
5. Since 1 hour is divided into 60 minutes, 0.4 of an hour is equal to 0.4 * 60 = 24 minutes.
6. Therefore, they would finish working on the manuscript at 2:24 PM.
To find out what time Julie and Pat would finish working together, we need to determine how long it would take them to complete the manuscript when they work together.
We can calculate their combined typing speed by adding up the rates at which they individually type. Julie takes 4 hours to type up the manuscript, which means she types at a rate of 1/4 (one manuscript per 4 hours). Similarly, Pat takes 6 hours, so his typing rate is 1/6 (one manuscript per 6 hours).
To find their combined typing rate, we add up their individual rates. So, 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Therefore, when Julie and Pat work together, they can type up 5/12 of the manuscript per hour.
Now, let's calculate how long it would take them to complete the entire manuscript by dividing the total work (1 manuscript) by their combined rate (5/12 manuscript per hour).
1 / (5/12) = 12/5 = 2.4 hours.
Convert 0.4 hours into minutes: 0.4 * 60 = 24 minutes.
So, when Julie and Pat work together, they can finish typing the manuscript in 2 hours and 24 minutes.
If they start working together at 12:00 pm, we add 2 hours and 24 minutes to determine the finish time.
12:00 pm + 2 hours and 24 minutes = 2:24 pm.
Therefore, they would finish at 2:24 pm.