Time Rate Problem help please............
- Thread starter puzzled01
- Start date
Hi, puzzled01!
...\(\displaystyle t\,=\,tyrone's\;time\,,\,m = mary's\;time\)
Since Mary can do it in 34.63 hours, we can fill that in for \(\displaystyle m\):\(\displaystyle \L \;\frac{1}{34.65}\,+\,\frac{1}{t}\,=\,\frac{1}{16}\)
Now we solve for \(\displaystyle t\). This is an ugly answer.
Subtract \(\displaystyle \frac{1}{34.65}\) from both sides:\(\displaystyle \L \;\frac{1}{t}\,=\,\frac{0.0336233035}{1}\;\Rightarrow\;t\,=\,\frac{1}{0.0336233035}\)
Since they make 1 computer program in 16 hours, we know mary's time for 1 computer program and we want to find tyrone's time for 1 comp. prog... you can make this equation:\(\displaystyle \L \;\frac{1}{m}\,+\,\frac{1}{t}\,=\,\frac{1}{16}\)
...\(\displaystyle t\,=\,tyrone's\;time\,,\,m = mary's\;time\)
Since Mary can do it in 34.63 hours, we can fill that in for \(\displaystyle m\):\(\displaystyle \L \;\frac{1}{34.65}\,+\,\frac{1}{t}\,=\,\frac{1}{16}\)
Now we solve for \(\displaystyle t\). This is an ugly answer.
Subtract \(\displaystyle \frac{1}{34.65}\) from both sides:\(\displaystyle \L \;\frac{1}{t}\,=\,\frac{0.0336233035}{1}\;\Rightarrow\;t\,=\,\frac{1}{0.0336233035}\)
Let us not make this nasty...
If Mary can do the job alone in 34.63 hours, then in 1 hour, Mary does 1/34.63 of the job.
Let t = number of hours it takes Tyrone to do the job alone. Then, in 1 hour, Tyrone does 1/t of the job.
Now...they're working together. It takes them 16 hours together. So, in 16 hours, Mary does 16/34.63 of the job, and Tyrone does 16/t of the job.
Mary's part of the job + Tyrone's part of the job = whole job
16/34.63 + 16/x = 1
Multiply both sides by the common denominator of the fractions, which is 34.63x:
34.63x(16/34.63) + 34.63x(16/x) = 34.63x*1
16x + 34.63*16 = 34.63x
I don't think this is a particularly "ugly" problem to solve.....
If Mary can do the job alone in 34.63 hours, then in 1 hour, Mary does 1/34.63 of the job.
Let t = number of hours it takes Tyrone to do the job alone. Then, in 1 hour, Tyrone does 1/t of the job.
Now...they're working together. It takes them 16 hours together. So, in 16 hours, Mary does 16/34.63 of the job, and Tyrone does 16/t of the job.
Mary's part of the job + Tyrone's part of the job = whole job
16/34.63 + 16/x = 1
Multiply both sides by the common denominator of the fractions, which is 34.63x:
34.63x(16/34.63) + 34.63x(16/x) = 34.63x*1
16x + 34.63*16 = 34.63x
I don't think this is a particularly "ugly" problem to solve.....