Question

1. a bicycle left the park and went north at 20 km/h. one hour later a motorcycle left the same place in the same direction at 25 km/h. after how many hours did the motorcycle overtake the bicycle?

Explanation:

Step1: Define variables

Let \( t \) be the time (in hours) the motorcycle travels until it overtakes the bicycle. Then the bicycle travels for \( t + 1 \) hours.

Step2: Set up distance equations

The distance traveled by the bicycle is \( d_{bicycle}=20(t + 1) \) (since distance = speed × time). The distance traveled by the motorcycle is \( d_{motorcycle}=25t \). When the motorcycle overtakes the bicycle, their distances are equal, so we set up the equation:

$$ 20(t + 1)=25t $$

Step3: Solve the equation

First, expand the left - hand side:

$$ 20t+20 = 25t $$

Then, subtract \( 20t \) from both sides:

$$ 20=25t - 20t $$

$$ 20 = 5t $$

Finally, divide both sides by 5:

$$ t=\frac{20}{5}=4 $$

Answer:

The motorcycle overtakes the bicycle after 4 hours.