Question

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.​

Answer 1

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