Grades 7-8 Video Solutions 2022-2022_7-8

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Question 20. Mark always bikes at the same speed, and he always walks at the same speed. He can cover the round trip from his home to the school and back again in 20 minutes  when he bikes, and in 60 minutes when he walks. Yesterday, Mark started biking to school, but stopped and left his bike at Eva's house  on the way before finishing his trip to school on foot. On the way back, he walked to Eva's house, picked up his bike, and then biked the rest of the way home.  His total travel time was 52 minutes. What fraction of his trip did Mark make by bike? So we can start off by recognizing that he bikes at a pace of 20 minutes, and he walks  at a pace of 60 minutes. So let's call the amount of time that he spent biking, B, and it'll be 20 times B minutes.  The amount of times that he spent walking will be 60 times the difference of 1 and B minutes.  We know that the total is 52 minutes, so we can set it equal to the sum of these two things. We can simplify this to 20B plus 60 minus 60B equal to 52.  We can simplify this by subtracting 60 from both sides, getting negative 8, and we can subtract 60B from 20B, getting negative 40B.  When we simplify this, we get B equal to 8 divided by 40, which is the fraction of the trip that Mark makes by bike.  When we simplify 8 divided by 40, we get our answer, which is B, 1 fifth.

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