Algebra 2

posted by .

Your car gets 25 mi/gal around town and 30 mi/gal on the highway.

a. If 50% of the miles you drive are on the highway and 50% are around town, what is your overall average miles per gallon?

b. If 60% of the miles you drive are on the highway and 40% are around town, what is your overall average miles per gallon?

  • Algebra 2 -

    a. Since the miles are equal, then you can just average your gas mileage.

    b. This will be a weighted average.
    Say you travel 100 miles.

    60(30) + 40 (25) =

    Divide that answer by 100.

  • Algebra 2 -

    if you drive c city miles and h highway miles, the gas you use is

    c/25 + h/30 gallons

    so, for a 50-50 mix

    100mi/(50/25+50/30)gal = 27.27 mi/gal

    and for a 40-60 mix

    100mi/(40/25+60/30)gal = 27.77 mi/gal

    extra credit:
    So, what would the mix have to be to get 29 mi/gal?

  • Algebra 2 -

    JJ's solution sounds simple, but the reality is not. This is just like the usual work problems. If A can do a job in 2 days, and B can do it in 4 days, you can't just average 2 and 4 to get 3 days.

    Instead, 1/both = 1/A + 1/B = 1/2 + 1/4 = 3/4

    So, together they do the job in 4/3 days.

    Makes sense, since A alone can do it in 2 days, any help from B will reduce the time it takes, not average out to 3 days.

    Same for the gas mileage.

    50 miles at 25gal/mi = 2 gal
    50 miles at 30mi/gal = 1.6667 gal

    so, 100 miles takes 3.6667 gal, or 27.27 mi/gal

  • Algebra 2 -

    Thank you so much, Steve!!!! I really appreciate your help!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    An automobile computer gives a digital readout of fuel consumption in gallons per hous. During a trip, a passenger recorded the fuel consumption every 5 minutes for a full hour of travel. time: 0 / gal/h: 2.5 time: 5 / gal/h: 2.4 time: …
  2. Math - Linear Equations

    A car gets 21 mi/gal in city driving and 28 mi/gal highway driving. If 18 gal of gas are used in traveling 448 mi, how many miles were driven in the city, how many driven on the highway (assuming that only the given rates of usage …
  3. Math

    tyler is looking at a map. he wants to stop at 3 towns on highway 57. Town a is 15 miles from town b. Town A is 26 miles from town c. Town b is between towns a and c. how many miles are between towns b and c?
  4. math

    One day we decided to drive from Town A to Town D. In order to get there we had to drive through Town B and then Town C. It is 10 miles farther from Town A to Town B than it is from Town B to C. IT is 10 miles farther from Town B to …
  5. Math

    Could someone answer this question so I understand it. The answer is 28.0, but i'd like to know how to do it. Thanks Randomly selected cars were weighed, and the highway fuel consumption amounts (in miles/gal) were determined. For …
  6. Math

    One day we decided to dive from town A to town B. In order to get there we had to drive through town B and then town C. it is 10 miles farther from town A to town B then it is to town B to C. It is 10 miles farther from town B to town …
  7. Math

    One day we decidid to drive from town A to town D.In order to get there,we had to drive through town B and C.It is ten miles farther from town A to town B than it is from town B to town C.It is ten miles farther from town B to town …
  8. word problem

    Millwood city is constructing a new highway through town. The construction crew can complete 5 3/6 miles of road each month. The total new highway will be 54 miles long. Will the highway be finished in 8 months?
  9. Math

    Rochelle's car average 32.5 miles per gallon the highway.At that rate,how many gallons of gas will her car use for driving on the highway for 260 miles?
  10. Algebra

    My car gets 13 miles per gallon in the city and 30 miles per gallon on the highway. Suppose I used 15.867 gallons of gas and got an average of 15 miles per gallon for the trip.

More Similar Questions