First, we convert all given mixed numbers into improper fractions. The fuel burned is 2(2)/(5) = (2 × 5 + 2)/(5) = (12)/(5) gallons, and the total time is 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) minutes.

First, we convert all given mixed numbers into improper fractions. The fuel burned is 2(2)/(5) = (2 × 5 + 2)/(5) = (12)/(5) gallons, and the total time is 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) minutes.

To find the rate per unit minute, divide the fuel used, (12)/(5) gallons, by the time taken, (3)/(10) minute. Dividing by a fraction is equivalent to multiplying by its reciprocal, which gives (12)/(5) × (10)/(3) = 4 × 2 = 8 gallons per minute.

To find the rate per unit minute, divide the fuel used, (12)/(5) gallons, by the time taken, (3)/(10) minute. Dividing by a fraction is equivalent to multiplying by its reciprocal, which gives (12)/(5) × (10)/(3) = 4 × 2 = 8 gallons per minute.

Multiply the burning rate of 8 gallons per minute by the total time of (3)/(2) minutes. We have 8 × (3)/(2) = 4 × 3 = 12 gallons.

A rocket test model burns fuel at a constant rate. It uses 2 2/5 gallons of fuel every 3/10 of a minute. How many gallons of fuel will it burn in 1 1/2 ?

Answer: 12 gallons

Step-by-step solution

Step 1: Convert mixed numbers to improper fractions

First, we convert all given mixed numbers into improper fractions. The fuel burned is $2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$ gallons, and the total time is $1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$ minutes.

Step 2: Find the fuel consumption rate per minute

To find the rate per unit minute, divide the fuel used, $\frac{12}{5}$ gallons, by the time taken, $\frac{3}{10}$ minute. Dividing by a fraction is equivalent to multiplying by its reciprocal, which gives $\frac{12}{5} \times \frac{10}{3} = 4 \times 2 = 8$ gallons per minute.

Step 3: Calculate fuel burned in the given time

Multiply the burning rate of $8$ gallons per minute by the total time of $\frac{3}{2}$ minutes. We have $8 \times \frac{3}{2} = 4 \times 3 = 12$ gallons.

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