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A 13km stretch of road needs repairs. Workers can repair 3(1)/(2)km of road per week. How many weeks will it take to repair this stretch of road? weeks

A 13 km 13 \mathrm{~km} stretch of road needs repairs. Workers can repair 312 km 3 \frac{1}{2} \mathrm{~km} of road per week.\newlineHow many weeks will it take to repair this stretch of road?\newlineweeks

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Full solution

Q. A 13 km 13 \mathrm{~km} stretch of road needs repairs. Workers can repair 312 km 3 \frac{1}{2} \mathrm{~km} of road per week.\newlineHow many weeks will it take to repair this stretch of road?\newlineweeks
  1. Given Data: We have:\newlineTotal length of road to repair: 13 km13\,\text{km}\newlineRepair rate per week: 312 km3\frac{1}{2}\,\text{km} or 3.5 km3.5\,\text{km}\newlineIdentify the values of total length and repair rate per week.\newlineTotal length (L)=13 km(L) = 13\,\text{km}\newlineRepair rate per week (R)=3.5 km(R) = 3.5\,\text{km}
  2. Find Weeks: We need to find:\newlineTotal number of weeks WW required to repair the 1313km stretch of road.\newlineIdentify the formula to calculate the total number of weeks.\newlineThe formula is W=LRW = \frac{L}{R}.\newlineSubstitute L=13L = 13km and R=3.5R = 3.5km in W=LRW = \frac{L}{R}.\newlineW=133.5W = \frac{13}{3.5}
  3. Calculate Weeks: Let's simplify the division to find the number of weeks.\newlineCalculate 13/3.513 / 3.5.\newline13/3.5=3.71428571…13 / 3.5 = 3.71428571\dots\newlineSince the number of weeks must be a whole number, we round up because workers cannot repair a fraction of a week.\newlineW=4W = 4
  4. Final Result: The total number of weeks required to repair the 1313km stretch of road is 44 weeks.

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