what is the domain?

Question

On a trip of d miles to another city, a truck driver's average speed was x miles per hour. On the return trip, the average speed was y miles per hour. The average speed for the round trip was 60 miles per hour.

(a) Verify that y = 30x/x-30

what is the domain in interval notation?

Answer 1

Distance=2d

Time going is d/x

Time returning is d/y

Average speed is 2d/[(d/x)+(d/y)]=60

The d's cancel and xy/(x+y)=30 -> y=30x/(x-30)

Since y must be positive, x must be greater than 30 and although mathematically x could go to infinity,

that makes no physical sense.