# 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?

Result

t =  17 h
s =  360 km

#### Solution:

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

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