Multiple choice

Asher goes to his tuition academy, 'Guidance Heart,' daily by running. One day, he ran at a speed of 10 miles per hour and reached his academy late by 20 minutes. The next day, he ran at a speed of 15 miles per hour and reached early by 15 minutes. What is the distance that he runs daily between his house and his academy?

  1. 17.5 miles

  2. 18.5 miles

  3. 19 miles

  4. 20 miles

  5. 22.5 miles
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Time 1 = D/10, Time 2 = D/15. Difference in time = 20 min + 15 min = 35 min = 35/60 hours. D/10 - D/15 = 35/60. (3D - 2D)/30 = 35/60. D/30 = 35/60. D = 17.5 miles.

AI explanation

Let the exact required time to reach the academy be T hours, so running at 10 miles per hour makes the time T plus one-third of an hour, while 15 miles per hour makes it T minus one-fourth of an hour. Because the distance is constant, we equate the distances using speed multiplied by time to get 10 multiplied by (T plus one-third) equals 15 multiplied by (T minus one-fourth). Solving this equation yields T equals 1.5 hours, and substituting this back gives the distance as 10 multiplied by (1.5 plus 0.333), which equals 17.5 miles.

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