Interpreting '310 of a minute' as (3)/(10) minute and '112' as 1(1)/(2) = (3)/(2) minutes, the burning rate is 750 gallons per minute. Multiplying this constant rate by 1.5 minutes gives 1125 gallons.

Interpreting '310 of a minute' as (3)/(10) minute and '112' as 1(1)/(2) = (3)/(2) minutes, the burning rate is 750 gallons per minute. Multiplying this constant rate by 1.5 minutes gives 1125 gallons.

If the numbers are taken literally as 225 gallons every 310 minutes over a duration of 112 minutes, the constant rate is (45)/(62) gallons per minute. Multiplying by 112 minutes yields (2520)/(31) gallons, which is approximately 81.29 gallons.

If the numbers are taken literally as 225 gallons every 310 minutes over a duration of 112 minutes, the constant rate is (45)/(62) gallons per minute. Multiplying by 112 minutes yields (2520)/(31) gallons, which is approximately 81.29 gallons.

A rocket test model burns fuel at a constant rate. It uses 225 gallons of fuel every 310 of a minute. How many gallons of fuel will it burn in 112 ?

Answer: Under the fractional interpretation ( $\frac{3}{10}\text{ min}$ and $1\frac{1}{2}\text{ min}$ ), the fuel burned is $1125\text{ gallons}$ . Under the literal integer interpretation ( $310\text{ min}$ and $112\text{ min}$ ), the fuel burned is $\frac{2520}{31}\text{ gallons} \approx 81.29\text{ gallons}$ .

Step-by-step solution

Step 1: Analyze the given rate problem and identify potential interpretations

The problem presents numbers with possible typographical variations common in scanned fraction texts (where $\frac{3}{10}$ might be printed as $310$ , and $1\frac{1}{2}$ or $112$ could represent the target time). We examine both standard interpretations: the fractional rate interpretation where fuel is burned at $225\text{ gallons}$ per $\frac{3}{10}\text{ minute}$ over $1\frac{1}{2}\text{ minutes}$ , and the literal integer reading of $225\text{ gallons}$ every $310\text{ minutes}$ over $112\text{ minutes}$ .

Step 2: Calculate burn rate and total fuel for the standard fraction interpretation

Interpreting '310 of a minute' as $\frac{3}{10}\text{ minute}$ and '112' as $1\frac{1}{2} = \frac{3}{2}\text{ minutes}$ , the burning rate is $750\text{ gallons per minute}$ . Multiplying this constant rate by $1.5\text{ minutes}$ gives $1125\text{ gallons}$ .

Step 3: Calculate burn rate and total fuel for the literal integer interpretation

If the numbers are taken literally as $225\text{ gallons}$ every $310\text{ minutes}$ over a duration of $112\text{ minutes}$ , the constant rate is $\frac{45}{62}\text{ gallons per minute}$ . Multiplying by $112\text{ minutes}$ yields $\frac{2520}{31}\text{ gallons}$ , which is approximately $81.29\text{ gallons}$ .

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