Afamily has two cars. during one particular week, the first car consumed 15 gallons of gas and the second consumed 35 gallons of gas. the two cars drove a
combined total of 1700 miles, and the sum of their fuel efficiencies was 60 miles per gallon. what were the fuel efficiencies of each of the cars that week?

Fuel efficiencies of two cars in that week are 20 miles per gallon and 40 miles per gallon.

Solution:

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.

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step-by-step explanation: