Accelerating-hour car — arithmetic increase of 5 km/h per hour: A car starts at 40 km/h and increases its speed by 5 km/h at the end of every hour. How many hours are required to cover 385 km?
Aptitude
Time and Distance
Difficulty: Medium
Choose an option
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A8.5 h
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B9.5 h
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C9 h
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D7 h
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E6.5 h
Answer
Correct Answer: 7 h
Explanation
Introduction / Context:Hourly changing speed implies the distance covered each hour forms an arithmetic progression (AP). Summing the AP until the total reaches 385 km yields the number of hours.
Given Data / Assumptions:
- Hour 1: 40 km
- Each next hour: +5 km
- Total distance: 385 km
Concept / Approach:Let n be hours. Distance = n/2 * (first + last) = n/2 * (40 + (40 + 5(n − 1))). Solve for n.
Step-by-Step Solution:
Total = n/2 * (80 + 5n − 5) = (5n^2 + 75n)/2Set (5n^2 + 75n)/2 = 385 ⇒ 5n^2 + 75n = 770Divide 5: n^2 + 15n − 154 = 0Discriminant = 841 = 29^2 ⇒ n = (−15 + 29)/2 = 7Verification / Alternative check:Distances per hour: 40, 45, 50, 55, 60, 65, 70 sum to 385 km.
Why Other Options Are Wrong:They do not satisfy the AP sum to 385 km.
Common Pitfalls:Using geometric growth instead of arithmetic growth or mis-summing the series.
Final Answer:7 h