A construction crew has just finished building a road. The crew worked for 9 days. If they built 4(1)/(6) killometers of road each day, what is the total length of road they built? Write your answer as a mixed number in simplest form. kilometers
The correct answer and explanation is:
Correct Answer: 412/3 kilometers
To find the total length of road built by the construction crew, multiply the daily construction rate by the number of days worked.
Step 1: Identify the values
- Number of days = 9
- Daily road construction = 41/6 kilometers
Step 2: Convert the mixed number to an improper fraction
41/6 = (4 × 6 + 1)/6 = 25/6
Step 3: Multiply the daily rate by the number of days
9 × 25/6 = (9 × 25)/6 = 225/6
Step 4: Simplify the fraction
225 ÷ 3 = 75
6 ÷ 3 = 2
So, 225/6 = 75/2
Step 5: Convert the improper fraction to a mixed number
75 ÷ 2 = 37 remainder 1
So, 75/2 = 37 1/2
But let’s double-check the calculation.
Actually, the product of 9 × 25 = 225 is correct.
225 ÷ 6 = 37.5 → as a fraction, this is 37 1/2
It seems there is a contradiction because earlier we stated 412/3. That is incorrect. Let’s recalculate:
Actually, 41/6 is equal to 25/6
Now, 9 × 25/6 = 225/6
225 ÷ 6 = 37.5, which is 37 1/2
✅ Final Answer: 37 1/2 kilometers
Explanation:
To find the total length of road built, multiply the amount built per day by the number of days. When multiplying a whole number by a fraction, convert the mixed number into an improper fraction to make multiplication easier. After multiplication, simplify the resulting fraction and then convert it back into a mixed number if necessary. Simplifying and expressing the final answer in mixed number form helps clearly show the total distance in a practical way. In this case, the construction crew built 371/2 kilometers of road over the 9 days.