Time Rate Problem help please............

[puzzled01]

Mary and Tyrone work for a computer software company. Together they can write a particular type of computer program in 16 hours. Mary can write the program by herself in 34.63 hours. How long will it take Tyrone to write the program alone?

 

[jonboy]

Hi, puzzled01!

Together they can write a particular type of computer program in 16 hours. Mary can write the program by herself in 34.63 hours. How long will it take Tyrone to write the program alone?

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:\(\displaystyle \L \;\frac{1}{t}\,=\,\frac{0.0336233035}{1}\;\Rightarrow\;t\,=\,\frac{1}{0.0336233035}\)

 

[galactus]

Yes, jonboy, it is rather homely. You could write it in fraction form.

\(\displaystyle \L\\\frac{20}{693}+\frac{1}{t}=\frac{1}{16}\)

\(\displaystyle \L\\\frac{1}{t}=\frac{373}{11088}\)

 

[jonboy]

Yeah. Galactus has a much better way. Thanks for the final touch!

 

[Mrspi]

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.....

 

[Denis]

29 hours, 43 minutes, 35.54959764... seconds :shock:

.54959764.... is endless, so does that mean poor Tyrone will never finish :wink:

 

[galactus]

I don't think this is a particularly "ugly" problem to solve.....

Jonboy didn't mean it was ugly to solve, but that the decimals were 'ugly'.
Fractions look better.