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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?



Answer :

Answer: 27 miles

Step-by-step explanation:

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​=47​Now, we can solve for dd. Let's find a common denominator for the fractions:4d108+3d108=741084d​+1083d​=47​Combining the fractions:7d108=741087d​=47​Now, cross multiply:7d×4=108×77d×4=108×728d=75628d=756Divide both sides by 28:d=75628d=28756​d=27d=27So, the distance between Darren's home and school is 27 miles

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