Question 4 Mark this question To collect data on the signal strengths in a neighborhood, Briana must drive from house to house and take readings. She has a graduate student, Henry, to assist her. Briana figures it would take her 12 hours to complete the task working alone, and that it would take Henry 18 hours if he completed the task by himself. How long will it take Briana and Henry to complete the task together? 4.5 hours 7.2 hours 6.7 hours 5.6 hours

When Briana and Henry work together, their rates of completing the task combine. Briana can finish the job in 12 hours, giving her a work rate of 1/12 of the task per hour. Henry, taking 18 hours, has a work rate of 1/18 of the task per hour. Together, their combined work rate is (1/12 + 1/18). To solve it, find a common denominator (which is 36), so you have (3/36 + 2/36) = 5/36 of the task per hour. Therefore, it would take them 36/5, or 7.2 hours to complete the task together. To ensure accuracy in collaborative tasks, always double-check your combined rates. A common mistake is to overlook the need for a common denominator when adding rates, leading to a miscalculation of time. So, keep your fractions in check to avoid running up against errors in collaborative projects!