Question

Gage skated $1$ hr $15$ min each day for $5$ days and $1$ hr $30$ min each day for $3$ days. How long would he have to skate the ninth day in order to average $85$ minutes of skating each day for the entire time?

$1$ hr

$1$ hr $10$ min

$1$ hr $20$ min

$1$ hr $40$ min

$2$ hr

Solution:

Gage has skated a total of $5 \cdot 75 + 3 \cdot 90 = 645 \text{ min.}$

For an average of $85$ minutes over $9$ days, Gage must have skated a total of $85 \cdot 9 = 765 \text{ min.}$

This means that Gage must skate $765 - 645 = 120 \text{ min.}$ on the last day. Note that $120$ minutes is the same as $2$ hours.

Thus, E is the correct answer.

2002 AMC 8 Problem 18

Solution:

Problem 18 in Other Years