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?

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

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 = 7 Verification / 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

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?

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