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.