2020 AMC 10A Problem 4

The question asks for dollars per hour, so it is easiest to look at just one hour of driving.

1. In one hour she drives $60$ miles.
2. She is paid $\$0.50$ per mile, so she earns $60 \times 0.50 = \$30$.
3. Her car goes $30$ miles on one gallon, so $60$ miles uses $60 \div 30 = 2$ gallons.
4. Gas costs $\$2.00$ per gallon, so she spends $2 \times 2.00 = \$4$.
5. What she keeps in that hour is $30 - 4 = \$26$.

The answer is $\boxed{\textbf{(E)}\ 26}$.

Everything here grows at a steady rate with time: twice the hours means twice the miles, pay and gas. So the $2$ hours do not change the rate per hour. Picking the time unit that the question asks about saves a division at the end.

Do the whole trip. In $2$ hours she drives $120$ miles and earns $120 \times 0.50 = \$60$. She uses $120 \div 30 = 4$ gallons, costing $\$8$. She keeps $60 - 8 = \$52$ over $2$ hours, which is $52 \div 2 = \$26$ per hour.

Since the answer is a rate per hour, look at a single hour of driving.

In one hour she covers $60$ miles and earns $60 \cdot 0.50 = 30$ dollars.

Those $60$ miles use $\frac{60}{30} = 2$ gallons of gasoline, costing $2 \cdot 2.00 = 4$ dollars.

Net pay per hour: $30 - 4 = 26$ dollars.

The answer is $\boxed{\textbf{(E)}\ 26}$.