A man runs a distance of 9km at a constant speed for the ...
A man runs a distance of 9km at a constant speed for the first 4 km and then 2 km\h faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4 km is
6 km/h
8 km/h
9 km\h
11 km\h
13 km\h
Correct answer is B
Let the average speed for the first 4 km = x km/h.
Hence, the last 5 km, speed = (x + 2) km/h
Recall: Time=DistanceSpeed
Total time = 1 hour.
∴
\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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