<u>Answer: </u>
Fuel efficiencies of two cars in that week are 20 miles per gallon and 40 miles per gallon.
<u>Solution: </u>
Let the two cars of family be A and B.
Gas consumed by car A = 15 gallons
Gas consumed by car B = 35 gallons
Let’s assume number of miles car A drove in that week = x miles
Assume number of miles car B drove in that week = y miles
Given that two cars drove a combine of 1700 miles in that week.
So we can say,
x + y = 1700 --- eqn (1)
Fuel efficiency of any car =
So fuel efficiency of car A =
And fuel efficiency of car B =
Given that sum of efficiencies of two cars = 60 miles per gallons.
On cross-multiplication we get,
5(7x +3y) =
7x +3y = 6300 --------- eqn (2)
Now we have following two equations and two variable to be determine.
x + y = 1700 -------- (1)
7x +3y = 6300 -------- (2)
On modifying equation (1) we get
y = 1700 - x --------(3)
On substituting value of y from equation (3) in equation (2) we get
7x + 3(1700-x) = 6300
7x + 5100 – 3x = 6300
4x = 6300 – 5100
4x = 1200
x = 300
Substituting value of x in equation 3 to get value of y
y = 1700 – 300 = 1400
Fuel efficiency of car A = =
= 20 miles per gallon
Fuel efficiency of car B = =
= 40 miles per gallon.
Hence fuel efficiencies of two cars in that week are 20 miles per gallon and 40 miles per gallon.