Pick the right reference frame and one of the moving things stops. The whole problem becomes a single object moving relative to a fixed point.
Method · Relative Motion
Intro
When two objects are moving and the question is about their encounter — meeting, overtaking, lapping, the gap between them — switch into one object’s frame and only track the difference. The recipe: (i) name the two motions and their directions, (ii) combine speeds — add if approaching, subtract if same direction (with the current adding/subtracting for swims and escalators), (iii) apply distance = (relative speed) × time. The same recipe handles clock hands, trains, river crossings, and walkers on escalators.
✓ Intro · expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine — being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
✓ Try first · expand
Worked example
A traditional clock’s hour and minute hands align exactly at 12:00 midnight. (a) When do they next coincide? (b) How many times do they overlap in a 24-hour period?
✓ Worked example · expand
Practice 1 of 3Type a fraction, decimal, or expression — mathjs parses it.
✓ Practice · expand
Reflection
Why does the bee problem collapse from an infinite zig-zag sum to a single multiplication? What is the general lesson about which <em>frame of reference</em> a problem secretly wants you to use — and how do you spot the cue in the problem statement?