Given Data

1. Time interval: Between 7 o'clock and 8 o'clock.
2. Target angle: 180 degrees.

Question

At what time between 7 and 8 o'clock will the hands of a clock be in a straight line pointing in opposite directions?

Answer

5 5/11 minutes past 7.

Solution

1. Set up the formula: |30H - 5.5M| = 180.
2. Substitute H = 7: |30(7) - 5.5M| = 180 => |210 - 5.5M| = 180.
3. Solving 210 - 5.5M = 180 gives 5.5M = 30.
4. M = 30 / 5.5 = 60 / 11 = 5 5/11 minutes.
5. Therefore, the hands are opposite each other at 5 5/11 minutes past 7.