Club members wrote a program together, with several people working on each of 4 parts. If the first part of the program required 1/3 of the total time, the second part needed 1/2 of the remaining time, the third part took 30 minutes, and the fourth part took 60 minutes, how many hours did the program take to write?

To find the total time it took to write the program, we need to calculate the time required for each part and then add them all together.

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.

To find out how many hours the program took to write, we need to calculate the total time spent on each part separately and then add them together.

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.

1/3x + 1/2x + 30 + 60 = x

Change fractions to common denominator and solve for x.