Three machines, X, Y, and Z, can complete a task in 8 hours, 10 hours, and 12 hours, respectively. If they start working one after the other (X, then Y, then Z), how long will it take to complete the task?(APPROX)

To solve this problem, we need to find out how much of the task each machine can complete in one hour, then add these amounts together to find out how much of the task all three machines can complete in one hour.

1. Machine X can complete 1/8 of the task in one hour.
2. Machine Y can complete 1/10 of the task in one hour.
3. Machine Z can complete 1/12 of the task in one hour.

If we add these together, we get:

(1/8) + (1/10) + (1/12) = 15/120 + 12/120 + 10/120 = 37/120

So, together, the three machines can complete 37/120 of the task in one hour.

However, the machines are not working together, they are working one after the other. This means that in the first hour, machine X completes 1/8 of the task, in the second hour, machine Y completes 1/10 of the task, and in the third hour, machine Z completes 1/12 of the task.

So, in three hours, the machines complete:

(1/8) + (1/10) + (1/12) = 37/120 of the task.

This cycle repeats every three hours. To find out how long it takes to complete the task, we need to find out how many times this cycle needs to repeat.

The task is completed when the sum of the fractions is equal to 1 (or as close to 1 as possible without going over).

So, we divide 1 by (37/120) to find out how many cycles are needed:

1 / (37/120) = 120/37 = approximately 3.24

This means that it takes approximately 3.24 cycles to complete the task. Since each cycle is 3 hours, we multiply 3.24 by 3 to find out how many hours it takes to complete the task:

3.24 * 3 = approximately 9.72 hours.

So, it takes approximately 9.72 hours for the three machines to complete the task when working one after the other.

Sure, I can help with that. Here's how you can solve this problem:

Step 1: Find the rate at which each machine can complete the task. The rate is simply 1 divided by the time it takes to complete the task. So, for machine X, the rate is 1/8 tasks per hour. For machine Y, the rate is 1/10 tasks per hour. And for machine Z, the rate is 1/12 tasks per hour.

Step 2: Add up the rates to find the combined rate. The combined rate is (1/8 + 1/10 + 1/12) tasks per hour.

Step 3: To find the total time it takes for all three machines to complete the task, divide 1 by the combined rate. This gives you the total time in hours.

Let's do the calculations:

Step 1: The rates are 1/8, 1/10, and 1/12 tasks per hour.

Step 2: The combined rate is (1/8 + 1/10 + 1/12) = 0.2083 tasks per hour.

Step 3: The total time is 1 / 0.2083 = 4.8 hours.

So, it will take approximately 4.8 hours for all three machines to complete the task if they start working one after the other.