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Select the correct answerThe speed of the car increases by 2 km/h after every one hour. If the distance covered in the first hour was 35 km, then what was the total distance covered in 12 hours?Options650 km560 km58 km552 km

Question

Select the correct answerThe speed of the car increases by 2 km/h after every one hour. If the distance covered in the first hour was 35 km, then what was the total distance covered in 12 hours?Options650 km560 km58 km552 km

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Solution

This problem can be solved using the formula for the sum of an arithmetic series.

The speed of the car increases by 2 km/h every hour, so the speeds at which the car travels each hour form an arithmetic sequence: 35, 37, 39, ..., for 12 terms.

The sum S of the first n terms of an arithmetic sequence can be found using the formula S = n/2 * (a + l), where:

  • n is the number of terms,
  • a is the first term, and
  • l is the last term.

In this case:

  • n = 12 (the car travels for 12 hours),
  • a = 35 km/h (the speed during the first hour), and
  • l = 35 + 2*(12 - 1) = 57 km/h (the speed during the 12th hour).

Substituting these values into the formula gives:

S = 12/2 * (35 + 57) = 6 * 92 = 552 km.

So, the car covered a total distance of 552 km in 12 hours. Therefore, the correct answer is 552 km.

This problem has been solved

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