Multiple choice

John departed from his residence at 8:30 am to attend a business meeting scheduled for 9:45 am. Driving for 40 minutes at an average speed of 25 miles per hour, he recognized that he was behind schedule. To compensate for the delay, he boosted his speed by 30% and managed to arrive precisely on time. What is the distance between John's house and the place of business meeting?

  1. 25.625 miles

  2. 30.5 miles

  3. 32.625 miles

  4. 35.625 miles

  5. 45.625 miles
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial speed = 25 mph. Time = 40 mins = 2/3 hours. Distance = 25 * 2/3 = 50/3 miles. Time remaining = 9:45 - 8:30 = 75 mins. Time spent = 40 mins. Time left = 35 mins. New speed = 25 * 1.3 = 32.5 mph. Distance covered in 35 mins = 32.5 * (35/60) = 32.5 * (7/12) = 18.958 miles. Total distance = 16.66 + 18.958 = 35.625 miles.

AI explanation

John drives for 40 minutes, which is 2/3 of an hour, at 25 miles per hour, so using the formula Distance equals Speed multiplied by Time, he covers 50/3 miles. He departs at 8:30 am and arrives at 9:45 am, meaning his total travel time is 75 minutes (or 5/4 hours), leaving exactly 35 minutes (which is 7/12 hours) for the remainder of the journey. His increased speed is 25 plus 30 percent of 25, equaling 32.5 miles per hour, so the second part of the distance is 32.5 multiplied by 7/12, which equals 227.5/12 miles. Adding the two distances of 50/3 miles and 227.5/12 miles gives a total distance of 427.5/12 miles, which simplifies to 35.625 miles. The result is 35.625.

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