The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{60} \) = \( \frac{\frac{28}{4}}{\frac{60}{4}} \) = \( \frac{7}{15} \)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{56}{12} \) = 4\(\frac{2}{3}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

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