SOLUTION: Jessica can wash the family dog in 45 minutes. Her brother can wash the dog in just 30 minutes. How long would it take them working together to wash the dog ?

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Question 1108568: Jessica can wash the family dog in 45 minutes. Her brother can wash the dog in just 30 minutes. How long would it take them working together to wash the dog ?
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Jessica's rate of washing:
[ 1 dog washed ] / [ 45 min ]
Brother's rate of washing:
[ 1 dog washed ] / [ 30 min ]
Their rate working together:
[ 1 dog washed ] / [ t min ]
---------------------------
Add their rates of washing to get rate
washing together
+1%2F45+%2B+1%2F30+=+1%2Ft+
Multiply both sides by +90t+
+2t+%2B+3t+=+90+
+5t+=+90+
+t+=+18+
It will take them 18 min working together

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The tutor @josmiceli has a great solution. Here's another way to look at it.

Let's say that instead of washing the dog, Jessica and her brother are washing a load of dishes. It can be any number of dishes, but I'm going to pick the number 90. Why 90? Because this is the LCM (lowest common multiple) of 45 and 30.

If Jessica can wash 90 dishes in 45 minutes, then she washes 2 dishes per minute (90/45 = 2). If her brother can wash 90 dishes in 30 minutes, then he can wash 3 dishes per minute (90/30 = 3). The question is: how many minutes will it take for them both to get all 90 dishes washed? This is assuming they divide the chore in a way where they wash their own set of dishes without any kind of overlap. Also, the assumption is that one person doesn't slow down or hinder the other.

In one minute, Jessica can wash 2 dishes. So in x minutes, she can wash 2*x dishes. Similarly, her brother can wash 3*x dishes in that time span of x minutes. In total, they can wash 2*x+3*x = 5*x dishes for that same time span. The goal is to wash all 90 dishes, so 5*x = 90. When solved for, we end up with x = 18 (divide both sides by 5)

It takes 18 minutes for the two siblings to wash the dishes together. This idea can be applied to washing the dog as well. So that's why it takes 18 minutes for Jessica and her brother to wash the dog if they work together.