SOLUTION: During the first 30 miles of city driving, you average 40 miles per hour. For the remainder of the trip, you drive on a highway at a constant rate of 85 miles per hour. Your averag

Algebra ->  Length-and-distance -> SOLUTION: During the first 30 miles of city driving, you average 40 miles per hour. For the remainder of the trip, you drive on a highway at a constant rate of 85 miles per hour. Your averag      Log On


   

Question 1156291: During the first 30 miles of city driving, you average 40 miles per hour. For the remainder of the trip, you drive on a highway at a constant rate of 85 miles per hour. Your average speed for the entire trip is given by
r(x) = (30 + x)/3/4+1/85x

where x is the number of miles you have driven on the highway.
(a) How far will you need to drive on the highway to bring your average speed up to 60 miles per hour?
Found 2 solutions by josgarithmetic, maurik34:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You want to show your function as r(x) = (30 + x)/(3/4+x/85). 
PART      SPEED       TIME        DISTANCE

first       40         30/40        30

last       85          x/85         x

TOTALS              x/85+3/4      x+30

function for average rate r for whole trip:
r%28x%29=%28x%2B30%29%2F%28x%2F85%2B3%2F4%29

With algebra steps, rewritten as r%28x%29=%28340x%2B10200%29%2F%284x%2B255%29

To answer the question "a", let r(x) equal 60, and solve the equation for x.

Answer by maurik34(1) About Me  (Show Source):
You can put this solution on YOUR website!
Thank you.The answer is 51.