Denise has 5 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 9mph and walks back at a speed of 3mph, how long should she plan to spend walking back?

To solve this problem, we can use this formula d = rd (distance = rates x time) She runs at a speed of 9 mph and walks at a speed of 3 mph. Her distance running is d = 9tr where tr is the time she spends running Her distance walking is d = 3tw where tw is the time she spends walking The distances are the same so 9tr = 3tw We also know that the total time is 5 hours tr + tw = 5 tr = 5-tw Substitute this value of tr in the first equation 9tr = 3tw 9 (5-tw) = 3tw 45-9tw = 3tw 45 = 12tw 3.75 = tw Denise will spend 3.75 hours (3 hours, 45 minutes) walking back and 1.25 hours (1 hour, 15 minutes) running.