WMC 2018 Senior Problem 25

Level 2

In a 3 3 mile race, Annabelle finishes ahead of Betty by 1 2 \frac{1}{2} mile and Betty finishes ahead of Carol by 1 4 \frac{1}{4} mile. Assuming all the runners run at constant speeds, how many miles did Annabelle finish ahead of Carol?

17 24 \frac{17}{24} 3 8 \frac{3}{8} 3 4 \frac{3}{4} 19 24 \frac{19}{24} 2 3 \frac{2}{3}

Tiger Ang by Tiger Ang , 20, Malaysia

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1 solution

X X
Oct 19, 2018

Annabelle's speed:Betty's speed = 3 : 2.5 = 72 : 60 =3:2.5=72:60

Betty's speed:Carol's speed = 3 : 2.75 = 60 : 55 =3:2.75=60:55

So, Annabelle's speed:Betty's speed:Carol's speed = 72 : 60 : 55 =72:60:55

When Annabelle runs 3 3 miles, Carol runs 3 × 55 72 = 55 24 3\times\frac{55}{72}=\frac{55}{24}

3 − 55 24 = 17 24 3-\frac{55}{24}=\frac{17}{24}

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