A driver averaged 60 miles per hour on a road trip from Santa Cruz to Los Angeles which is nearly 300 miles away.

Question

The average speed for going was x and the average speed for returning was y.

(Hint: a 600 mile trip averaging 60 miles per hour means 10 total hours)

a. Using Distance/Rate=Time formula, show that: y = 30x/(x - 30)

b. Complete the following table using the function above
X(mph): 40 45 50 55 60 65 70 (Given)
Y(mph): 120 90 75 66 60 55 52 (correct?)

And when the function is graphed, what does the Asymptotes mean in the context of this problem
and is it possible to average 25 miles per hour in one direction?

Answer 1

Just translating your English information into Math:
300/x + 300/y = 10 , (the hint told us that the total time was 10 hrs.)

30/x + 30/y = 1
multiply each term by xy, the LCD
30y + 30x = xy
30x = xy - 30y
30x = y(x-30)
y = 30x/(x-30) , as required

b) Just testing two of your results
(45,90)
LS = 90
RS = 30(45)/(45-30) = 90, correct

(65,55)
LS = 55
RS = 30(65)/(65-30) = 55.714.. ≠ LS , INCORRECT

Suppose he goes 25 mph one way, that would take 300/25 or 12 hours
BUT, to average 60 mph for the whole return trip has to take 10 hours.
We already used up all our time just going one way.
Answer is NO!