Betty paints twice as fast as Dan. Working together Dan and Betty can paint, $2,400$ square feet in $4$ hours. Another employee sue, joined their painting team. Working together, Dan, Betty and Sue can paint $3,600$ square feet in 3 hours.
if Sue works alone, how many square feet can she paint in $4$ hours $27$ minutes.
I am really struggling with these word problems, I have tried to set it out first but fail miserably!
for example
if betty paints twice as fast as dan than would this equation be valid
$2B + D = 2,400$ ? But how do i include the time element? I cant seem to form the equations for time and work separately, and than link them
$\endgroup$ 12 Answers
$\begingroup$Given that Dan and Betty can paint $2400$ sq. ft in $4$ hours. They can paint $\dfrac{2400}{4}=600$ sq ft in one hour.
Since given that Betty can paint twice as fast as dan, let us take the equation as $p+2p=600\implies p=\dfrac{600}{3}=200$
So, Dan can paint $200$ sq ft in $1$ hour. Betty can paint twice so, $400$ sq ft
Now, Betty, Dan and sue can paint $3600$ sq ft in $3$ hours.
So, Sue can paint $600$ sq ft in an hour.
Now you can easily find the painting done by Sue in $4$ hours $27$ minutes.
$\endgroup$ 3 $\begingroup$You should be trying to compute the number of square feet per hour that each one can do. When Dan and Betty work together, she does $2/3$ of the work. How many square feet does she do? Given that she works for $4$ hours, how many does she do per hour? Once you find the missing number, you should be able to compute Sue's painting rate.
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