A motorist goes at a speed of 30 km/h reaches his destination 40 minutes late.…
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A motorist goes at a speed of 30 km/h reaches his destination 40 minutes late. Next time he increases his sped by 5 km/h but still he is late by 15 minutes. Find the distance of the office from his home.
Answer: B. 87.5 km — Let the distance be d km. Time taken at 30 km/h = d/30 hours. This arrival is 40 minutes late, so actual time − scheduled time = 40/60 hours. Time taken at 35…
- A.
75 km
- B.
87.5 km
- C.
55 km
- D.
67.5 km
Attempted by 38 students.
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Correct answer: B
Let the distance be d km.
Time taken at 30 km/h = d/30 hours. This arrival is 40 minutes late, so actual time − scheduled time = 40/60 hours.
Time taken at 35 km/h = d/35 hours. This arrival is 15 minutes late, so actual time − scheduled time = 15/60 hours.
The difference between the two travel times equals the difference in lateness: d/30 - d/35 = (40/60) - (15/60) = 25/60 hours.
Compute the left side: 1/30 - 1/35 = (35 - 30)/(30·35) = 5/1050 = 1/210. So d*(1/210) = 25/60.
Solve for d: d = (25/60) × 210. Since 210/60 = 3.5, d = 25 × 3.5 = 87.5.
Therefore the distance from home to office is 87.5 km.