Working together, Daniel and Donnie can clean the llama pen in 50 minutes. On his own, Daniel can clean the pen in 90 minutes. How long does it take Donnie to clean the llama pen on his own?

112.5 minutes

Step-by-step explanation:

Working together, Daniel and Donnie can clean the llama pen in 50 minutes. On his own, Daniel can clean the pen in 90 minutes.

Let the number of minutes it takes Donnie to clean his Ilama pen be represented by: x

Hence, we have the expression:

1/90 + 1/x = 1/50

The Lowest Common Denominator for the left hand side = 90x

Hence:

x + 90/90x = 1/50

Cross Multiply

50(x + 90) = 90x

50x + 4500 = 90x

Collect like terms

4500 = 90x - 50x

4500 = 40x

Divide both sides by 40

x = 4500/40

x = 112.5 minutes

Therefore, it takes Donnie 112.5 minutes to clean the llama pen on his own.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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