A person traverses a certain distance in 1 hour 24 minutes by covering…
2022
A person traverses a certain distance in 1 hour 24 minutes by covering two-thirds of the distance at 4 km per hour and the rest at 5 km per hour. Find the distance covered by the person.
Answer: A. 6 km — ConceptFor a journey split into parts, total time is the sum of the time for each part. For any part, time equals distance divided by speed, so the same…
- A.
6 km
- B.
8 km
- C.
6.5 km
- D.
7 km
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
For a journey split into parts, total time is the sum of the time for each part. For any part, time equals distance divided by speed, so the same unknown total distance must be used consistently in every segment.
Application
Let the total distance be d km. The given total time is 1 hour 24 minutes = 84/60 = 7/5 hours.
The first segment is 2d/3 km at 4 km/h, so its time is (2d/3) ÷ 4 = d/6 hours.
The remaining segment is d/3 km at 5 km/h, so its time is (d/3) ÷ 5 = d/15 hours.
Therefore d/6 + d/15 = 7/5. Combining the fractions gives 7d/30 = 7/5, so d = 6 km.
Cross-check
For 6 km, two-thirds is 4 km and the remainder is 2 km. These take 4/4 = 1 hour and 2/5 hour = 24 minutes, for a total of 1 hour 24 minutes.
Hence, the distance covered is 6 km.