2002 AMC 8 Problems/Problem 18

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?

$\text{(A)}\ \text{1 hr}\qquad\text{(B)}\ \text{1 hr 10 min}\qquad\text{(C)}\ \text{1 hr 20 min}\qquad\text{(D)}\ \text{1 hr 40 min}\qquad\text{(E)}\ \text{2 hr}$

Solution

Converting into minutes and adding, we get that she skated $75*5 +90*3 +x=375 +270 +x=645 +x$ minutes total, where x is the amount she skated on day 9. Dividing by 9 to get the average, we get $\frac{645+x}{9}=85$ . Solving for x, $645+x=765$ $x=120$ Now we convert back into hour and minute to get 2 hours. $\text{(E)}$

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2002 AMC 8 Problems/Problem 18

Solution