4. After just 4 tenths of a 2.5 -mile race was completed, Lenox took the lead and remained there until the end of the race. a. How many miles did Lenox lead the race? b. Reid, the second-place finisher, developed a cramp with 3 tenths of the race remaining. How many miles did Reid run withnut

To solve this problem, we need to calculate the distance Lenox led the race and the distance Reid ran without cramping. Given: - The race is 2.5 miles long. - Lenox took the lead after 4 tenths of the race was completed. - Reid developed a cramp with 3 tenths of the race remaining. a. To find out how many miles Lenox led the race, we need to calculate the distance Lenox covered after taking the lead. Distance covered by Lenox after taking the lead = Total race distance - Distance covered by Lenox before taking the lead Distance covered by Lenox before taking the lead = 4 tenths of 2.5 miles Distance covered by Lenox after taking the lead = 2.5 miles - 4 tenths of 2.5 miles b. To find out how many miles Reid ran without cramping, we need to calculate the distance Reid covered before developing a cramp. Distance covered by Reid before developing a cramp = Total race distance - Distance covered by Reid after developing a cramp Distance covered by Reid after developing a cramp = 3 tenths of 2.5 miles Distance covered by Reid before developing a cramp = 2.5 miles - 3 tenths of 2.5 miles Let's calculate these distances. Calculate the value by following steps: - step0: Calculate: \(2.5-\frac{4}{10}\times 2.5\) - step1: Reduce the fraction: \(2.5-\frac{2}{5}\times 2.5\) - step2: Multiply the numbers: \(2.5-1\) - step3: Subtract the numbers: \(1.5\) The distance Lenox led the race is 1.5 miles. Now, let's calculate the distance Reid ran without cramping. Calculate the value by following steps: - step0: Calculate: \(2.5-\frac{3}{10}\times 2.5\) - step1: Multiply the numbers: \(2.5-\frac{3}{4}\) - step2: Convert the expressions: \(\frac{5}{2}-\frac{3}{4}\) - step3: Reduce fractions to a common denominator: \(\frac{5\times 2}{2\times 2}-\frac{3}{4}\) - step4: Multiply the numbers: \(\frac{5\times 2}{4}-\frac{3}{4}\) - step5: Transform the expression: \(\frac{5\times 2-3}{4}\) - step6: Multiply the numbers: \(\frac{10-3}{4}\) - step7: Subtract the numbers: \(\frac{7}{4}\) The distance Reid ran without cramping is 1.75 miles. Therefore, the answers to the questions are: a. Lenox led the race by 1.5 miles. b. Reid ran 1.75 miles without cramping.