Distance between points A and B = 90 km. A cyclist and a motorcyclist left point A at the same time.

Distance between points A and B = 90 km. A cyclist and a motorcyclist left point A at the same time. The speed of a motorcyclist is 40 km / h faster than that of a cyclist. Determine the speed of the cyclist if he arrived at point B 3 hours later than the motorcyclist.

Let’s write down the speed of the cyclist as x km / h.

Since the speed of the motorcyclist is 40 km / h more, it will be equal to: x + 40 km / h.

The motorcyclist traveled the entire distance in:

90 / (x + 40).

The cyclist covered the entire distance in:

90 / h.

The time difference will be:

90 / x – 90 / (x + 40) = 3.

90 * (x + 40) – 90 * x = 3 * x * (x + 40).

90 * x + 3600 – 90 * x = 3 * x ^ 2 + 120 * x.

3 * x ^ 2 + 120 * x – 3600 = 0.

x ^ 2 + 40 * x – 1200 = 0.

D ^ 2 = 1600 – 4 * 1 * (-1200) = 1600 + 4800 = 6400.

D = 80.

x = (-40 + 80) / 2 = 40/2 = 20 km / h (cyclist speed).

Answer:

Cyclist speed is 20 km / h.