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Question A construction company needs to remove 2562 \frac{5}{6} tons of dirt. They can remove 310\frac{3}{10} tons per hour. Find the total hours to remove the dirt, expressed as a simplified mixed number.

Studdy Solution

STEP 1

Assumptions
1. The total amount of dirt to be removed is 2562 \frac{5}{6} tons.
2. The company can remove 310\frac{3}{10} tons of dirt each hour.
3. The company works continuously without breaks.

STEP 2

First, we need to convert the mixed number to an improper fraction to make the calculation easier.
256=2×6+56=1762 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{17}{6}

STEP 3

Now, we need to find the total number of hours it will take to remove the dirt. We can do this by dividing the total amount of dirt by the amount of dirt that can be removed each hour.
Total hours=Total amount of dirtAmount of dirt removed per hourTotal\, hours = \frac{Total\, amount\, of\, dirt}{Amount\, of\, dirt\, removed\, per\, hour}

STEP 4

Plug in the given values for the total amount of dirt and the amount of dirt removed per hour to calculate the total hours.
Total hours=176310Total\, hours = \frac{\frac{17}{6}}{\frac{3}{10}}

STEP 5

When dividing fractions, we can multiply the first fraction by the reciprocal of the second fraction.
Total hours=176×103Total\, hours = \frac{17}{6} \times \frac{10}{3}

STEP 6

Multiply the fractions to find the total hours.
Total hours=17×106×3=17018Total\, hours = \frac{17 \times 10}{6 \times 3} = \frac{170}{18}

STEP 7

Simplify the fraction to its lowest terms.
Total hours=17018=859Total\, hours = \frac{170}{18} = \frac{85}{9}

STEP 8

Convert the improper fraction back to a mixed number to get the final answer.
Total hours=949Total\, hours = 9 \frac{4}{9}
The construction company will need 9499 \frac{4}{9} hours to remove the dirt.

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