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AMO 2027 Grades 9-11 SET 4 - Self-study Question 7

AMO · AMO 2027 Grades 9-11 SET 4 - Self-study

Question 7

Samuel cycles at constant speed along a straight street from $A$ to $B$. When he is $\frac6{19}$ of the way from $A$ to $B$, he hears a car approaching from behind $A$ at $418$ km/h. If he immediately turns back, he meets the car at $A$; if he continues toward $B$, the car overtakes him at $B$. How fast is Samuel cycling, in km/h?

Use the idealized source model: the car keeps its speed, and Samuel keeps the same speed in either direction, with no turning delay.

Enter one positive integer, without units.