A man runs a distance of 9km at a constant speed for the first 4…

A man runs a distance of 9km at a constant speed for the first 4 km and then 2 kmh faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4 km is

  • A.
    6 km/h
  • B.
    8 km/h
  • C.
    9 kmh
  • D.
    11 kmh
  • E.
    13 kmh
Correct Answer: Option B
Explanation

Let the average speed for the first 4 km = x km/h.

Hence, the last 5 km, speed = (x + 2) km/h

Recall: (Time = frac{Distance}{Speed})

Total time = 1 hour.

(therefore frac{4}{x} + frac{5}{x + 2} = 1)

(frac{4(x + 2) + 5x}{x(x + 2)} = 1)

(9x + 8 = x^{2} + 2x)

(x^{2} + 2x – 9x – 8 = 0 implies x^{2} – 7x – 8 = 0)

(x^{2} – 8x + x – 8 = 0)

(x(x – 8) + 1(x – 8) = 0)

(x = -1; x = 8)

Since speed cannot be negative, x = 8km/h.

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