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2020 AMC 10A Problem 4

Problem 4 of 25EasierAlgebra

A driver travels for 22 hours at 6060 miles per hour, during which her car gets 3030 miles per gallon of gasoline. She is paid $0.50\$0.50 per mile, and her only expense is gasoline at $2.00\$2.00 per gallon. What is her net rate of pay, in dollars per hour, after this expense?

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Solution

The driver travels 260=1202\cdot60=120 miles, so she is paid 120$0.50=$60120\cdot \$0.50=\$60. The trip uses 12030=4\frac{120}{30}=4 gallons of gasoline, costing 4$2=$84\cdot\$2=\$8. Her net pay is 608=5260-8=52 dollars over 22 hours, or 2626 dollars per hour. Thus, E is the correct answer.

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Concepts: rate · money

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.