# From point A to point B, the distance between which is 40 km / h, a motorist and a cyclist left at the same time.

From point A to point B, the distance between which is 40 km / h, a motorist and a cyclist left at the same time. It is known that a motorist travels 25 km more per hour than a cyclist. Determine the speed of a cyclist if it is known that he arrived at point B 1 hour 40 minutes later than the motorist.

1. The unit of measure for distance is indicated by mistake 40 km / h, you must specify 40 km.

2. Let x be the speed of the cyclist.

3.1 hour 40 minutes = 5/3 hours.

4. Let’s make the equation:

40 / x – 40 / (x + 25) = 5/3;

(40x + 1000 – 40x) / (x ^ 2 + 25x) = 5/3;

3000 = 5x ^ 2 + 125;

x ^ 2 + 25 – 600 = 0;

The equation has 2 solutions.

The first value x = (- 25 + √25 ^ 2 + 4 x 600) / 2 = (- 25 + 55) / 2 = 15 km / h.

The second value x = (- 25 – 55) / 2 = – 40. Does not satisfy the condition of the problem.

Answer: the speed of the cyclist is 15 km / h.

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