A school boy, travelling at 3 km/hr, reaches his school 28 minutes late but…
2024
A school boy, travelling at 3 km/hr, reaches his school 28 minutes late but when he travels at 5 km/hr, he reaches his school 28 minutes early. What distance does he travel every day to reach the school?
Answer: C. 7 km — ConceptFor a fixed distance d, travel time is t = d/v. If the same journey is late at one speed and early at another, the difference between the two travel…
- A.
6 km
- B.
8 km
- C.
7 km
- D.
9 km
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Concept
For a fixed distance d, travel time is t = d/v. If the same journey is late at one speed and early at another, the difference between the two travel times equals the sum of the lateness and earliness.
Application
Let the daily distance be d km. At 3 km/h, the travel time is d/3 hours; at 5 km/h, it is d/5 hours.
The total difference in arrival times is 28 + 28 = 56 minutes = 14/15 hour.
Therefore, d/3 - d/5 = 14/15.
Combining the fractions gives d(5 - 3)/15 = 14/15, so 2d/15 = 14/15.
Multiplying by 15 gives 2d = 14; hence d = 7 km.
Cross-check
For 7 km, the two travel times are 7/3 hours = 2 hours 20 minutes and 7/5 hours = 1 hour 24 minutes. Their difference is 56 minutes, so the scheduled arrival lies exactly 28 minutes between them.
Result: The daily distance to school is 7 km.