If a cyclist had travelled 5 km/h faster, she would have needed 1.5 hr less time to travel 150 km. Find the speed of the cyclist.
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Answer: The speed is 20 Km/h and the time is 7.5 hours
x = 20 km/h
t = 7.5 hours
Step-by-step explanation:
x = speed in km/h
t = time in hours
x * t = 150
(x + 5) * (t - 1.5) = 150
(x + 5) * (150 / x - 1.5) = 150
150 / x * x - 1.5x + 750 / x - 7.5 = 150
150 - 1.5x + 750 / x - 157.5 = 0
-1.5x + 750 / x - 7.5 = 0
-1.5x² + 750 - 7.5x = 0
x² + 5x - 500 = 0
Apply pq formula and you get:
x = -2.5 + 22.5
x = 20
x = -2.5 - 22.5
x = -25
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