Sophia Milestone 2 College Algebra With Correct Answers

Sophia Milestone 2 College Algebra With Correct Answers. To find how long it will take John to travel 50 miles, we can use the distance, rate, time formula and solve for time. Plug in 50 miles for the distance, and 40 miles per hour for the rate, or speed. Once we have plugged in the values, we need to write miles per hour as a fraction: 40 miles over 1 hour. When dividing by a fraction, we can change this into a multiplication problem and multiply by the reciprocal of 40 miles per 1 hour, which would be 1 hour over 40 miles. Rewrite 50 miles as a fraction over 1, and multiply this by the reciprocal of 40 mph. Next, multiply the numerators and denominators of the fractions. Multiplying across the numerator and denominator, produces 50 over 40. The units of miles cancel, so we are left with hours. Finally, divide 50 by 40. It will take John 1.25 hours. However, because we must express our answer in hours and minutes, we must convert 0.25 hours to minutes. Using the conversion factor, 60 minutes to 1 hour, evaluate the fractions by multiplying the numerators and denominators. Multiplying across the numerator and denominator produces 0.25 times 60, or 15. Units of hours cancel, leaving only minutes. It will take John 1 hour and 15 minutes to travel 50 miles at a constant speed of 40 miles per hour. CONCEPT Distance, Rate, and Time 4 The number of employees who will be able to perform a specific task is given by the equation , where N is the number of people who are able to perform the task, and t is time (in days). How long will it take until 100 employees are able to perform the task? 16 days 20 days 4 days 8 days RATIONALE The number of employees who can perform the task is modeled by this equation. To find how long it will take until 100 employees can perform the task, we will substitute this value for N and solve for t. Once N is replaced, we can solve for t. First, divide both sides by 25 to undo 25 multiplied by the square root of t. On the left, 100 divided by 25 is 4. To undo the square root of t on the right, square both sides. On the left, 4 squared is 16. It will take 16 days for 100 employees to be able to perform the task.