A cyclist left point A to point B. 2 hours later a motorcyclist followed him, whose speed is 36 km / h more than the speed

| January 15, 2021 | education

A cyclist left point A to point B. 2 hours later a motorcyclist followed him, whose speed is 36 km / h more than the speed of the cyclist. 0.5 hours after its departure, the motorcycle caught up with the cyclist. find the speed of the motorcyclist.

Introduce a variable, denote the speed of the cyclist as x, then the speed of the motorcyclist will be (x + 36).
The cyclist was on the road for 2 hours (before the motorcyclist left point A) + 0.5 hours (when the motorcyclist caught up with him) = 2.5 hours.
The motorcyclist was on the road for only 0.5 hours.
Let’s express the distance traveled by the cyclist: x * 2.5.
Let us express the distance traveled by the motorcyclist: (x + 36) * 0.5.
Since the distances traveled are equal, we make the equation:
2.5x = 0.5 (x + 36);
2.5x = 0.5x + 18;
2.5x – 0.5x = 18;
2x = 18;
x = 18/2 = 9 (km / h) – we found the speed of the cyclist.
The motorcyclist’s speed is 36 km / h more: 9 + 36 = 45 (km / h).
Answer: The motorcyclist’s speed is 45 km / h.



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