Use the function t(r) = d/r, where t is the time in hours, d is the distance in miles, and r is the rate in miles per hour. Sydney drives 10 mi at a certain rate and then drives 20 mi at a rate 5 mi/h faster than the initial rate. Write expressions for the time along each part of the trip. Add these times to write an equation for the total time in terms of initial rate, t Total (r).

Question

anonymous · Answer

well your 2 equations would be:

T = 10/r
and
T = 20/(r+5)

your question is using this info, how to find an equation for total time.

well total time would just be both equations added together. since both equations = T, you can just add them together.

10/r + 20/(r+5) = Total Time

anonymous · Answer

Okay, the next part of the problem asks me to determine any reasonable domain and range and describe any discontinuities of t Total (r). How do i do this?

anonymous · Answer

well, look at the denominator for each term. specifically, the 1/r and 1/r+5

remember, you cannot divide by zero. That means r cannot be what values?

anonymous · Answer

also, what makes sense for r?

r is the speed you are traveling at (assuming it's speed, not velocity)

is it possible to have a negative speed? does that make sense for r? or should it be only positive numbers?

anonymous · Answer

r cannot be -5 or 0. It should only be positive numbers.