1/3x + 1/2x + 30 + 60 = x
Change fractions to common denominator and solve for x.
Change fractions to common denominator and solve for x.
Let's start with the third part, which took 30 minutes.
Moving to the fourth part, which took 60 minutes, we now have a total time of 30 + 60 = 90 minutes.
Now, let's calculate the remaining time after the first two parts by subtracting 90 minutes from the total time:
Total time - Remaining time = 90 minutes
Total time - (1/3) x Total time - (1/2) x Remaining time = 90 minutes
Simplifying the equation, we get:
Total time - (1/3) x Total time - (1/2) x (Total time - Remaining time) = 90 minutes
Expanding the equation, we get:
Total time - (1/3) x Total time - (1/2) x Total time + (1/2) x Remaining time = 90 minutes
Combining like terms, we get:
Total time - (1/3 + 1/2) x Total time + (1/2) x Remaining time = 90 minutes
Finding a common denominator, we get:
Total time - (2/6 + 3/6) x Total time + (1/2) x Remaining time = 90 minutes
Simplifying, we get:
Total time - (5/6) x Total time + (1/2) x Remaining time = 90 minutes
To remove the fractions, we can multiply all terms by 6:
6 x Total time - 5 x Total time + 3 x Remaining time = 540 minutes
Simplifying, we get:
Total time + 3 x Remaining time = 540 minutes
Since we know that the remaining time is 90 minutes, we can substitute it into the equation:
Total time + 3 x 90 = 540 minutes
Simplifying, we get:
Total time + 270 = 540 minutes
To isolate the total time, we need to subtract 270 from both sides of the equation:
Total time = 540 - 270 minutes
Calculating, we find that the total time is:
Total time = 270 minutes
Since there are 60 minutes in an hour, we can convert the total time from minutes to hours:
Total time in hours = 270 minutes / 60 minutes/hour
Calculating, we find that the program took approximately 4.5 hours to write.
Therefore, the program took 4.5 hours to write.
Let's break down the problem step by step:
1. The first part of the program required 1/3 of the total time. Let's assume the total time spent on the program is represented by "x". Therefore, the first part of the program took (1/3) * x time.
2. The second part needed 1/2 of the remaining time after finishing the first part. After completing the first part, the remaining time is (x - (1/3)x). So, the second part took (1/2) * (x - (1/3)x) time.
3. The third part of the program took 30 minutes.
4. The fourth part took 60 minutes.
Now, let's add up the total time:
Total time = (1/3)x + (1/2) * (x - (1/3)x) + 30 minutes + 60 minutes
To convert the total time into hours, we need to divide it by 60 (as there are 60 minutes in an hour):
Total time in hours = (Total time) / 60
Let's calculate the total time:
Total time = (1/3)x + (1/2) * (x - (1/3)x) + 30 + 60
Simplifying the equation:
Total time = (1/3)x + (1/2)x - (1/6)x + 90
Combining like terms:
Total time = (2/6)x + (3/6)x + (1/6)x + 90
Total time = x + (1/6)x + 90
Simplifying further:
Total time = (7/6)x + 90
Now, let's convert the total time to hours:
Total time in hours = (Total time) / 60
Total time in hours = ((7/6)x + 90) / 60
We still need the value of "x" to get the final answer.
Unfortunately, the problem does not provide enough information to determine the exact value of "x." Without that information, we cannot calculate the exact number of hours the program took to write.