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

Answer:

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

Step-by-step explanation:

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

$20 \times 75 = 1500\; \text{miles}$.

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:

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

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

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