SOLUTION: I did a problem very similar to this one and I got it wrong. I really need help and I have to show all of my work! On a 1287 mile long trip in windy conditions, a family calcula

Question 864058: I did a problem very similar to this one and I got it wrong. I really need help and I have to show all of my work!
On a 1287 mile long trip in windy conditions, a family calculates their fuel economy to be 18 miles per gallon over the 2 days it takes to reach their destination. On their 2-day return trip, with similar wind at their backs, their calculations show a fuel economy of 26 miles per gallon.
#1 Calculate the expected fuel economy of their vehicle in ideal (non-windy) conditions (f) as well as the influence of the wind (w) in miles per gallons.
#2Compare how many gallons of fuel they used for the round trip to the expected usage in idea (non-windy) travel conditions. Which uses more? By how many gallons? Round to the nearest hundredth, if necessary?
Thnaks for any help!!!!!!!!
Found 2 solutions by richwmiller, josgarithmetic:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1287/18=71.5 gallons outgoing
1287/26=49.5 gallons incoming
22 gallons difference
11 gallons added against the wind and 11 gallons fewer with the wind
60.5 gallons with no wind 21.27 miles per gallon with no wind
2)
I would expect usage to average out with the wind and against the wind. Otherwise we have no way to calculate anything. Any differences comes from rounding off.

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Uniform rates problem, fuel efficiency.
Rv=d for Rate volume distance; distance in miles, volume in gallons.

__________________Rate__________volume__________distance
Going_____________18____________x_______________18x=1287
Returning_________26____________y_______________26y=1287

The volumes x and y can be easily calculated.
gallons, GOING;
gallons, RETURNING.

To look at the rates for wind-effect and fuel efficiency without the wind, try assigning variables r and w.
r = fuel efficiency without wind
w = the influence of the wind

______________Rate___________volume___________distance
GOING_________r-w____________71.5_____________1287
RETURN________r+w____________49.5_____________1287

This arrangement gives also two equations in the two unknowns, now r and w.
This system:

and

-
The volumes were already found from x and y in the previous part of the problem.
The rest of the work for r and w are for you to finish.
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