a painter can paint a wall in 8 hours with help of an assistant they can finish in 5 hours how long would it take the assistant alone to paint the wall
Answer (1)
Answer:13hours and 20 minutesStep-by-step explanation:To solve this problem, we can use the concept of work rates. Let's define the variables and follow the steps to find out how long it would take the assistant to paint the wall alone.Step 1: Define the work ratesPainter's work rate: The painter can paint the wall in 8 hours. Therefore, the painter's work rate is:Painter’s rate= 8 hours1 wall = 81 walls per hourCombined work rate: When the painter and the assistant work together, they can finish the wall in 5 hours. Therefore, their combined work rate is:Combined rate= 5 hours1 wall = 51 walls per hourAssistant's work rate: Let the assistant's work rate be r (walls per hour).Step 2: Set up the equationWhen the painter and the assistant work together, their work rates add up:Painter’s rate+Assistant’s rate=Combined rateSubstituting the known values:81 +r= 51 Step 3: Solve for the assistant's work rateTo solve for r, we need to isolate it:Subtract the painter's rate from both sides:r= 51 − 81 Find a common denominator to subtract the fractions. The least common multiple of 5 and 8 is 40:51 = 408 81 = 405 Now substitute these values into the equation:r= 408 − 405 = 403 Step 4: Calculate the time for the assistant to paint the wall aloneThe assistant's work rate is 403 walls per hour. To find out how long it takes the assistant to paint one wall, we take the reciprocal of the work rate:Time for assistant= r1 wall = 403 1 = 340 hoursStep 5: Convert to hours and minutesTo convert 340 hours into hours and minutes:Divide 40 by 3:40÷3=13.33 hoursThe whole number part is 13 hours.To find the minutes, take the decimal part (0.33) and multiply by 60:0.33×60≈20 minutesFinal AnswerIt would take the assistant approximately 13 hours and 20 minutes to paint the wall alone.
