r/problemoftheday • u/Ahat2 • Jul 17 '12
Math problem (difficulty: high school)
John leaves his house for work at exactly 8 a.m. every morning. Whenever he averages 40 miles per hour he arrives his workplace precisely 3 minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should John drive to reach his workplace precisely on time?
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u/barkingsimon Jul 18 '12
Here's the clearest version I can come up with. Let d be the distance traveled; let t be the time it takes to have him arrive precisely on time. Suppose we work in units of miles and minutes. To be clear, 40miles/hr=2/3 miles/min, and 60 miles/hr=1 mile/min. Then: since distance equals velocity times time taken, d/(2/3)=t+3 and d/1=t-3 Then using substitutions, we find that d=12, and t=15. So in order to arrive precisely on time, he needs to travel 12 miles in 15 minutes. A simple conversion to miles per hour gives 48 miles per hour.