A watch gains 5 seconds every 3 minutes. It was set right at 7:00 A.M. the same day. In the afternoon, when the watch shows 4:15 P.M., what is the true time?

Problem restatement
The watch runs fast: it gains 5 s every 3 minutes. After it shows 4:15 P.M., find the true clock time.

Given data

• Gain = 5 s per 3 min.
• Set right at 7:00 A.M.; indicated time later is 4:15 P.M.

Concept/Approach
In 3 true minutes (180 s), the watch indicates 185 s. Hence the indicated-to-true time ratio is 185:180 = 37:36. So true elapsed time = indicated elapsed × (36/37).

Step-by-step calculation
Indicated elapsed from 7:00 A.M. to 4:15 P.M. = 9 h 15 m = 555 minutes True elapsed = 555 × (36/37) minutes Since 555/37 = 15, true elapsed = 15 × 36 = 540 minutes = 9 hours True time = 7:00 A.M. + 9:00 = 4:00 P.M.

Verification/Alternative
Forward check: Over 9 true hours, the watch gains (9 h × 60/3)×5 s = 180×5 s = 900 s = 15 min. Thus it would indicate 9 h 15 m → 4:15 P.M. (consistent).

Common pitfalls

• Subtracting 15 minutes directly from the indicated time without aligning start time and total elapsed.

Final Answer
4:00 P.M.