Ivan trained for a cross-country meet.

On Monday, he ran a certain distance.

On Tuesday, he ran twice as far as he ran on Monday.

On Wednesday, he ran half as far as he ran on Tuesday.

On Thursday, he ran half as far as he ran on Wednesday.

On Friday, he ran twice as far as he ran on Thursday.

If the shortest distance that he ran on any of the five days is $5 \mathrm{~km}$, how far did he run in total?
(A) $55 \mathrm{~km}$
(B) $25 \mathrm{~km}$
(C) $27.5 \mathrm{~km}$
(D) $17.5 \mathrm{~km}$
(E) $50 \mathrm{~km}$
Suppose that Ivan ran a distance of $x \mathrm{~km}$ on Monday.

Then on Tuesday, he ran $2 x \mathrm{~km}$, on Wednesday, he ran $x \mathrm{~km}$, on Thursday, he ran $\frac{1}{2} x \mathrm{~km}$, and on Friday he ran $x \mathrm{~km}$.

The shortest of any of his runs was on Thursday, so $\frac{1}{2} x=5$ or $x=10$.

Therefore, his runs were $10 \mathrm{~km}, 20 \mathrm{~km}, 10 \mathrm{~km}, 5 \mathrm{~km}$, and $10 \mathrm{~km}$, for a total of $55 \mathrm{~km}$.

ANSWER: (A)