Together, Raquel and Miray can spread the mulch through the yard in 2 hours. Raquel would take 0.8 times as many hours as Miray would take to spread the mulch alone. How long would it take Miray to spread the mulch alone? hours

Question

Bytelearn · Accepted Answer

Denote Time for Miray: Let's denote the time it takes for Miray to spread the mulch alone as M hours. According to the problem, Raquel would take 0.8 times as many hours as Miray to do the same job alone. Therefore, the time it takes for Raquel to spread the mulch alone is 0.8M hours.Time for Raquel: Since Raquel and Miray can spread the mulch together in 2 hours, we can use the formula for work done together: (1/M) + (1/(0.8M)) = 1/2, where (1/M) is the part of the work Miray does in one hour and (1/(0.8M)) is the part of the work Raquel does in one hour. The right side of the equation represents the part of the work they complete together in one hour.Work Done Together: Now we need to solve the equation for M. Let's find a common denominator for the fractions on the left side of the equation: (1/M) + (1/(0.8M)) = 1/2. The common denominator for M and 0.8M is 0.8M. We rewrite the equation as (0.8/0.8M) + (1/0.8M) = 1/2.Solve for M: Simplify the fractions on the left side of the equation: (0.8 + 1) / 0.8M = 1/2. This simplifies to (1.8) / 0.8M = 1/2.Cross-Multiply: To solve for M, we cross-multiply: 1.8 * 2 = 0.8M * 1. This gives us 3.6 = 0.8M.Divide to Solve for M: Now, we divide both sides of the equation by 0.8 to solve for M: M = 3.6 / 0.8. This gives us M = 4.5.

Together, Raquel and Miray can spread the mulch through the yard in $2$ hours. Raquel would take $0$ . $8$ times as many hours as Miray would take to spread the mulch alone. $\newline$ How long would it take Miray to spread the mulch alone? $\newline$ hours

Full solution

More problems from Solve proportions: word problems

Related topics

Together, Raquel and Miray can spread the mulch through the yard in 222 hours. Raquel would take 000.888 times as many hours as Miray would take to spread the mulch alone.\newlineHow long would it take Miray to spread the mulch alone?\newlinehours

Together, Raquel and Miray can spread the mulch through the yard in $2$ hours. Raquel would take $0$ . $8$ times as many hours as Miray would take to spread the mulch alone. $\newline$ How long would it take Miray to spread the mulch alone? $\newline$ hours