2021 AMC 10 A Fall
Complete problem set with solutions and individual problem pages
Mr. Lopez has a choice of two routes to get to work. Route is miles long, and his average speed along this route is miles per hour. Route is miles long, and his average speed along this route is miles per hour, except for a -mile stretch in a school zone where his average speed is miles per hour. By how many minutes is Route B quicker than Route A?(2021 AMC Fall 10A, Question #4)
- A.
- B.
- C.
- D.
- E.
Solution 1:
If Mr. Lopez chooses Route , then he will spend hour, or minutes. If Mr. Lopez chooses Route , then he will spend hour, or minutes. Therefore, Route B is quicker than Route A by (B) minutes.
Solution 2:
We use the equation to solve this problem. Recall that 1 mile per hour is equal to mile per minute. For Route A, the distance is 6 miles and the speed to travel this distance is mile per minute. Thus, the time it takes on Route is 12 minutes. For Route , we have to use the equation twice: once for the distance of miles with a speed of mile per minute and a distance of miles at a speed of mile per minute. Thus, the time it takes to go on Route is minutes. Thus, Route is faster than Route A. Thus, the answer is (B) .
