If a person covers four-fifths of a circular track in m minutes, how many…
2019
If a person covers four-fifths of a circular track in m minutes, how many minutes will the person take to complete one full revolution at the same constant speed?
- A.
5m/(4π) minutes
- B.
(πm)/4 minutes
- C.
5m/4 minutes
- D.
4m/5 minutes
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
At a constant speed, time is directly proportional to distance. If a fraction f of a journey takes time t, the time for the whole journey is t/f.
Application
Let T be the time, in minutes, for one complete revolution.
Four-fifths of the track takes m minutes, so (4/5)T = m.
Divide both sides by 4/5: T = m/(4/5).
Dividing by a fraction means multiplying by its reciprocal, so T = m × 5/4 = 5m/4 minutes.
Cross-check
Four-fifths of 5m/4 is (4/5) × (5m/4) = m, which reproduces the given time.
Therefore, one complete revolution takes 5m/4 minutes.