A man travels from his home to his office at a speed of 4 km/h and reaches his…
2023
A man travels from his home to his office at a speed of 4 km/h and reaches his office 30 minutes late. If his speed had been 6 km/h, he would have reached office 5 minutes early. Find the distance of his office from his home.
Answer: B. 7 km — ConceptFor a fixed distance, travel time equals distance divided by speed. When the same journey is made at two speeds, the difference in travel times is…
- A.
8.5 km
- B.
7 km
- C.
8 km
- D.
9 km
Show answer & explanation
Correct answer: B
Concept
For a fixed distance, travel time equals distance divided by speed.
When the same journey is made at two speeds, the difference in travel times is distance multiplied by the difference of the reciprocals of the speeds.
Application
Let the home-to-office distance be d km. The travel times at 4 km/h and 6 km/h are d/4 hours and d/6 hours, respectively.
The first arrival is 30 minutes late and the second is 5 minutes early, so the first journey takes 30 + 5 = 35 minutes more. Thus, the time difference is 35/60 = 7/12 hour.
Therefore, d/4 - d/6 = 7/12.
Combining the fractions gives d(3 - 2)/12 = 7/12, so d/12 = 7/12 and d = 7 km.
Cross-check
For 7 km, the two travel times are 7/4 hour = 1 hour 45 minutes and 7/6 hour = 1 hour 10 minutes.
Their difference is 35 minutes, exactly the sum of 30 minutes late and 5 minutes early. Hence, the distance is 7 km.