Henry Ernest Dudeney/Puzzles and Curious Problems/62 - At Right Angles/Solution/Proof 2

Puzzles and Curious Problems by Henry Ernest Dudeney: $62$

At Right Angles

How soon between the hours of five and six will the hour and minute hands of a clock be exactly at right angles?

Solution

$10 \tfrac {10} {11}$ past $5$.

Proof

From Time when Hour Hand and Minute Hand at Right Angle, the times when this is between $5$ and $6$ are:

$05:10:55$

and:

$05:43:38$

The first of these is the earlier of those two times.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $62$. -- At Right Angles
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $54$. At Right Angles