# Motorcyclist

From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle?

Correct result:

t =  17 h
s =  360 km

#### Solution:

$\ \\ 60(t-11)=80 \cdot \ (t-12.50) \ \\ \ \\ 60 \cdot \ (t-11)=80 \cdot \ (t-12.50) \ \\ \ \\ 20t=340 \ \\ \ \\ t=17 \ \text{h}$
$s=60 \cdot \ (t-11)=60 \cdot \ (17-11)=360 \ \text{km}$

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