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To solve your questions, let's break it down step by step.

Part a: Time to complete one task

1. The robot completes 8 tasks in three-fourths of an hour (which is \( \frac{3}{4} \) hour).

2. To find the time taken for one task, we can divide the total time by the number of tasks.

   \[ \text{Time per task} = \frac{\text{Total time}}{\text{Number of tasks}} = \frac{\frac{3}{4} \text{ hour}}{8} \]

   This can be calculated as follows:

   \[ \text{Time per task} = \frac{3}{4} \div 8 = \frac{3}{4} \times \frac{1}{8} = \frac{3}{32} \text{ hour} \]

So, the robot takes \( \frac{3}{32} \) hour to complete one task.

Part b: Number of tasks in one hour

To find out how many tasks the robot can complete in one hour, we can use the fact that we know the time taken for one task.

1. If one task takes \( \frac{3}{32} \) hour, then the number of tasks that can be completed in one hour can be calculated as the reciprocal of the time per task:

   \[ \text{Number of tasks} = \frac{1 \text{ hour}}{\text{Time per task}} = \frac{1}{\frac{3}{32}} = \frac{32}{3} \]

   This simplifies to approximately 10.67 tasks, meaning the robot can complete about 10 full tasks in one hour, and will have used part of the hour for a 11th task.

Final answers:

a. It takes the robot \( \frac{3}{32} \) hour to complete one task.
b. The robot can complete approximately \( \frac{32}{3} \) or about 10.67 tasks in one hour.