Question

lamar takes \\(\frac{1}{4}\\) of an hour to complete \\(\frac{1}{2}\\) of his homework assignment. at this rate, how long will it take lamar to finish the homework assignment?
9.
karen drove \\(\frac{3}{4}\\) of a mile in \\(\frac{1}{60}\\) of an hour. at this rate, how many miles would she drive in one hour?

Explanation:

Problem 8 (Lamar's Homework)

Step1: Identify rate logic

To find time for full assignment, divide time by fraction of work done.

Step2: Perform division

Time for \(\frac{1}{2}\) work is \(\frac{1}{4}\) hour. So total time: \(\frac{1}{4} \div \frac{1}{2}\)
\[
\frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times 2 = \frac{1}{2}
\]

Step1: Identify rate formula

Rate (miles per hour) = distance ÷ time.

Step2: Substitute values

Distance = \(\frac{3}{4}\) mile, Time = \(\frac{1}{60}\) hour. So rate: \(\frac{3}{4} \div \frac{1}{60}\)
\[
\frac{3}{4} \div \frac{1}{60} = \frac{3}{4} \times 60 = 45
\]

Answer:

\(\frac{1}{2}\) hour

Problem 9 (Karen's Driving)