Question

A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During

one particular week, the two cars went a combined total of 1325 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of
the two cars that week?

Answer 1

• The
  `20` mile-per-gallon car consumed
  `40` gallons, whereas
• The
  `15` mile-per-gallon car consumed
  `35` gallons.

Explanation:

Assume that the
`20` mile-per-gallon car consumed all that
`75` gallons of fuel. How far would the cars have travelled?

`20 * 75 = 1500\; \text{miles}`.

This assumption overestimated the total mileage of the two cars by
`1500 - 1325 = 175\; \text{miles}`. Here's why: for every gallon that the second (
`15` mile-per-gallon) car consumed, this assumption would overestimate the total mileage by
`20 - 15 = 5\; \text{miles}`. Therefore, the overestimation of
`175\; \text{miles}` corresponds to:

`\begin{aligned} & 175\; \text{miles overestimated} \\ & * \left(\frac{1\; \text{gallon consumed by the second car}}{5\; \text{miles overestimated}}\right)\\ &= (175)/(5)\; \text{gallons consumed by the second car} \\ &= 35\; \text{gallons consumed by the second car}\end{aligned}`.

Therefore, the second car consumed
`35\; \text{gallons}`. The first car would have consumed
`75 - 35 = 40\; \text{gallons}`.

Verify the results:
`40 * 20 + 35* 15 = 1325\; \text{miles}`.