1) A runner and a cyclist start together from city $A$ heading to city $B$, which is $13 \mathrm{~km}$ away from $A$, with the agreement to shuttle between $A$ and $B$ without ever stopping. Knowing that the runner covers $9 \mathrm{~km}$ every hour while the cyclist covers 25 km, what distance will separate the two athletes after three hours from the start of the competition?
(A) $1 \mathrm{~km}$
(B) $2 \mathrm{~km}$
(C) $3 \mathrm{~km}$
(D) $4 \mathrm{~km}$
(E) $5 \mathrm{~km}$
1) The answer is (B)

After 3 hours, the runner will have traveled 27 km. Since 26 km correspond to the round trip between $A$ and $B$, he will be 1 km away from $A$. In the same time, the cyclist will have traveled $75 \mathrm{~km}$, three less than three times the round trip between $A$ and $B$, so he will be $3 \mathrm{~km}$ away from $A$. Their distance will thus be $3-1=2 \mathrm{~km}$.