Between 5:30 and 6:00, at what time will the hands of the clock be at right angles (90°)?

Problem restatementFind the exact time between 5:30 and 6:00 when the angle between the hands is 90°.

Given data

• At t minutes after 5, hour-hand angle = 150° + 0.5t°.
• Minute-hand angle = 6t°.
• Right angle → |difference| = 90°.

Concept/ApproachSolve |6t − (150 + 0.5t)| = 90 and select the solution between t = 30 and t = 60.

Step-by-Step calculation|5.5t − 150| = 90Case 1: 5.5t − 150 = 90 → t = 240 ÷ 5.5 = 43 7⁄11Case 2: 5.5t − 150 = −90 → t = 60 ÷ 5.5 = 10 10⁄11 (not in 5:30–6:00)Required time = 5 : 43 7⁄11

Verification/AlternativeRelative speed method confirms one valid right angle in this half-hour window.

Common pitfallsForgetting to restrict to the stated interval and accepting the earlier solution.

Final Answer5:43 7⁄11