Joan Bedney travels from Cincinnati to WinstonSalem at an average rate of 40 miles per hour and returns at an average rate of 60 miles per hour. What is her average speed for the trip? (Hint: The average speed is not 50 miles per hour.)
Answer given by text: 48.
The text is: Thanks, Belinda Hi Belinda,Suppose that the distance between the two cities is 120 miles. At 40 miles per hour it takes 3 hours to get there, and at 60 miles per hour it takes 2 hours to get back. Therefore Joan traveled 240 miles in 5 hours. What is her average speed? Do you see what is the trap? Calculate the proportion of time spent at each of the speeds. let t2 = the time at 60 mph let d = the distance between Cin and W.S. Using rate x time = distance we see that so 40 x t1 = 60 x t2 and solving for the time ratio we get t1/t2 = 60/40 or t1/t2 = 3/2 Now that we know the proportion, we see that 3/5 of the time for the trip was spent at 40 mph and 2/5 was spent at 60 mph. Thus the average speed is 3/5 x 40 + 2/5 x 60 = 48 mph. Cheers,Leeanne and Claude
