Darren drive to school in rush hour traffic and averages 27 mph. He returns home in mid-afternoon when there is less traffic and averages 36 mph. What is the distance between his home and school if the total traveling time is 1hr and 45 minutes?

Given that Darren travels to school in rush hour traffic at 27 mph and returns home in mid-afternoon at 36 mph, we can set up the following equations based on the time and speed relationship:d2727d (time taken to go to school)d3636d (time taken to return home)We know that the total traveling time is 1 hour and 45 minutes, which is equivalent to 7447 hours.So, we can write the equation:d27+d36=7427d+36d=47Now, we can solve for dd. Let's find a common denominator for the fractions:4d108+3d108=741084d+1083d=47Combining the fractions:7d108=741087d=47Now, cross multiply:7d×4=108×77d×4=108×728d=75628d=756Divide both sides by 28:d=75628d=28756d=27d=27So, the distance between Darren's home and school is 27 miles