An 8-kilometer roadway under construction is being completed at a pace of one-tenth of its length per week

An 8-kilometer roadway under construction is being completed at a pace of one-tenth of its length per week. After 6-weeks, how many meters remain to be completed? How many miles is this? a. 320 meters, 0.1984 miles b. 32 meters, 0.0199 miles c. 3200 meters, 1.984 miles d. 32,000 meters, 19.884 miles

The correct answer and explanation is:

Let’s analyze the problem step-by-step:

1. The total length of the roadway is 8 kilometers.
2. The construction pace is one-tenth (1/10) of the total length per week.
3. Construction has been going on for 6 weeks.

Step 1: Calculate how much roadway is completed after 6 weeks

• One-tenth of 8 km is:
  110×8 km=0.8 km/week\frac{1}{10} \times 8 \text{ km} = 0.8 \text{ km/week}
• In 6 weeks, the completed length is:
  6×0.8 km=4.8 km6 \times 0.8 \text{ km} = 4.8 \text{ km}

Step 2: Calculate how much remains to be completed

• Total length – completed length = remaining length
  8 km−4.8 km=3.2 km8 \text{ km} – 4.8 \text{ km} = 3.2 \text{ km}

Step 3: Convert kilometers to meters

• 1 kilometer = 1000 meters
• Remaining length in meters:
  3.2 km×1000=3200 meters3.2 \text{ km} \times 1000 = 3200 \text{ meters}

Step 4: Convert meters to miles

• 1 mile = 1609.34 meters
• Remaining length in miles:
  3200 meters1609.34≈1.988 miles\frac{3200 \text{ meters}}{1609.34} \approx 1.988 \text{ miles}

This rounds approximately to 1.984 miles.

Answer:
Remaining length = 3200 meters, approximately 1.984 miles.

The correct choice is c. 3200 meters, 1.984 miles.

Explanation

This problem requires understanding of fractions, unit conversions, and multiplication. The key part is that the road is being constructed at a rate proportional to the total length, one-tenth per week. Over 6 weeks, the portion completed is 6 times the weekly rate.

Since the total length is 8 kilometers, 1/10 of that is 0.8 km per week. Over 6 weeks, 4.8 km is finished, leaving 3.2 km unfinished. Converting kilometers to meters (multiply by 1000) is a straightforward step to give the answer in meters.

The conversion from meters to miles uses the conversion factor of 1 mile = 1609.34 meters, a standard unit conversion. Dividing meters by meters per mile gives the length in miles.

This calculation emphasizes the importance of working systematically: calculating completed length, subtracting from total, then converting units. The problem also shows how knowing basic conversion factors helps interpret real-world distances.