Problema Solution
A family has two cars. During one particular week, the first car consumed
20
gallons of gas and the second consumed
25
gallons of gas. The two cars drove a combined total of
775
miles, and the sum of their fuel efficiencies was
35
miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answer provided by our tutors
let
x = the fuel efficiency of the first car
d1 = the distance the first car traveled
y = the fuel efficiency of the second car
d2 = the distance the second car traveled
the sum of their fuel efficiencies was 35 miles per gallon
x + y = 35
the fuel efficiency is given as a ratio of distance traveled per unit of fuel consumed thus:
x = d1/20 follows d1 = 20x
y = d2/25 follows d2 = 25y
The two cars drove a combined total of 775 miles:
d1 + d2 = 775
20x + 25y = 775
by solving the system of equations:
x + y = 35
20x + 25y = 775
we find:
x = 20 mpg
y = 15 mpg
click here to see the step by step solution of the system of equations:
the fuel efficiency of the first car is 20 miles per gallon.
the fuel efficiency of the second car is 15 miles per gallon.