SOLUTION: Jim's car gets 26 miles per gallon on the highway and 18 miles per gallon in city traffic. He has 22 gallons of gasoline in his tank and is going on a trip. a. Write and express

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Question 1001317: Jim's car gets 26 miles per gallon on the highway and 18 miles per gallon in city traffic. He has 22 gallons of gasoline in his tank and is going on a trip.
a. Write and expression for the amount of gas Jim uses driving (h) highway miles and (c) city traffic miles.
b. Can Jim make a 480 mile trip consisting of 90 miles of city traffic without buying more gas? Explain your reasoning.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
RV=D relates fuel efficiency ( a rate ) with fuel volume and distance. This is a basic uniform rates situation.

If variables are c for miles in city driving, and h for miles in highway driving then you may arrange rv=c for city driving at rate r, and Rv=h for highway driving at rate R.

DATA TABLE USING VALUES DESCRIBED AND VARIABLES STILL NEEDED
             rate         volume(gallons)       distance (miles)
HIGHWAY      26              h/26                     h
CITY         18              c/18                     c
Total                         22

This gives a formula for volume of fuel used if h and c are both known.
h%2F26%2Bc%2F18=22



Question (b):
              rate           volume           distance
HWY            26             h/26              h
CTY            18             90/18              90
Total                          22              480

Make the obvious equations and see if they make sense together or what more the results mean.
h%2F26%2B90%2F18=22
h%2F26%2B5=22
h%2F26=17
h=17%2A26
highlight_green%28h=442%29--------the amount of highway distance possible. If you look at the sum h%2B90, as if h%2B90%3E=480. Is it true or not?
-
442%2B90%3E=480
532%3E=480---------certainly this is true.

Enough fuel, yes, for the 480 mile trip which includes 90 miles in the city.