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?

Difficulty: Medium

8.5 h
9.5 h
9 h
7 h
6.5 h

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 = 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.

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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