a driver averaged 50 miles per hour on the round trip between akron, oh and Columbus, oh, 100 miles away. The average speeds for going and returning were x and y miles per hour, respectively.

Question

a. show that y=25x/x-25

b. determine the vertical and horizontal asymptotes of the function.

c.using a graphing utility to graph the function

d. complete the table
x | 30 | 35 | 40 | 45 | 50 | 55 | 60|
y | | | | | | | |

Answer 1

time going = 100/x ---> from Time = distance/ rate
time going = 100/y

total time = 100/x + 100/y = (100y + 100x)/(xy)
total distance = 200

avg speed = total distance / total time
= 200/( (100y+100x)/(xy) )
= 200 (xy)/(100y+100x)
= xy/(y+x)
but avg speed = 50
xy/(x+y) = 50
xy = 50x + 50y
xy - 50y = 50x
y(x-50) = 50x
y = 50x/(x-50) ----> not your answer
( one of us made a mistake)

horizontal asymptote of my answer: y = 50
vertical asymptote of my answer: x = 50

Answer 2

went 200 miles total averaging 50mph so took 4 hours total

going: time = 100/x
returning time = 100/y
so
100/x + 100/y = 4

25/x + 25/y = 1

25 y + 25 x = xy

xy - 25 y = 25 x

y(x-25) = 25 x

y = 25 x /(x-25)

as x approaches 25, y becomes undefined, vertical asymptote

Answer 3

Damon, I am having a brain freeze.
I know you answer is correct.
Can you see the error in my solution?

Answer 4

Found my error.

from :
= 200 (xy)/(100y+100x)
= xy/(y+x)

should be
= 200 (xy)/(100y+100x)
= 2xy/(y+x)

Answer 5

Whew, sorry, did not see this until you found it.