Joan Bedney travels from Cincinnati to Winston-Salem 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.
Please tell us how they arrived at that answer. It's driving us crazier.

The text is:

Algebra 1 Merrill
Applications and Connections
Page 233 #38

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 t1 = the time at 40 mph
let t2 = the time at 60 mph
let d = the distance between Cin and W.S.

Using rate x time = distance we see that

40 x t1 = d and 60 x t2 = d
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.

Leeanne and Claude
Go to Math Central