if you complete 13%of a problem in 3 hrs how long will it take to get 100% of the problem completed?

If 13% of a problem is completed in 3 hours, we can calculate the time it will take to complete 100% of the problem by setting up a proportion of percent completed to number of hours.

Let x be the number of hours is takes to complete 100% of the problem, and write the percentages as decimals:

[tex]\dfrac{13\%}{3}=\dfrac{100\%}{x}\implies \dfrac{0.13}{3}=\dfrac{1}{x}[/tex]

Cross-multiply:

[tex]x\cdot 0.13 = 1 \cdot 3[/tex]

[tex]0.13x=3[/tex]

Now, solve for x by dividing both sides by 0.13:

[tex]\dfrac{0.13x}{0.13}=\dfrac{3}{0.13}[/tex]

[tex]x=23.0769230769...\; \sf hours[/tex]

[tex]x=23.08\; \sf hours\;(nearest\;hundredth)[/tex]

Therefore, it would take approximately 23.08 hours (23 hours 4 minutes 36 seconds) to complete 100% of the problem if the rate remained constant.