Math Problem Statement

Question content area top Part 1 A robot can complete 3 tasks in five sixths hour. Each task takes the same amount of time.

Solution

To find out how long it takes the robot to complete each task, we can follow these steps:

Step 1: Define the variables.

Let tt be the time (in hours) it takes the robot to complete one task.

The robot completes 3 tasks in 56\frac{5}{6} of an hour.

Step 2: Set up the equation.

If the robot completes 3 tasks in 56\frac{5}{6} hours, the time for one task is:

t=563t = \frac{\frac{5}{6}}{3}

Step 3: Solve for tt.

To divide by 3, multiply by the reciprocal:

t=56×13=518hourst = \frac{5}{6} \times \frac{1}{3} = \frac{5}{18} \, \text{hours}

Thus, each task takes 518\frac{5}{18} hours, or approximately 16.67 minutes.

Would you like more details on this or have any questions?


Here are 5 related questions:

  1. How long would it take the robot to complete 10 tasks at this rate?
  2. How many tasks can the robot complete in 1 hour?
  3. If the robot works for 2 hours, how many tasks will it complete?
  4. If the time per task decreases by half, how long would it take to complete 3 tasks?
  5. What if the robot had to complete 6 tasks in the same amount of time?

Tip: When dividing fractions, remember to multiply by the reciprocal of the divisor.

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Math Problem Analysis

Mathematical Concepts

Fractions
Division

Formulas

Time per task = Total time / Number of tasks
Division of fractions

Theorems

Reciprocal rule for division of fractions

Suitable Grade Level

Grades 6-8