Step-by-step explanation:
So we're trying to get from minutes to weeks. The time intervals in question are:
Minutes -> Hours -> Days -> Weeks
So we set up our dimensional analysis. We're solving for amount of problems, so that goes in the numerator of the first fraction:
[tex]\frac{1problem}{1.5min}[/tex]
Now we want to know how many minutes in an hour, so we multiply by the next fraction:
[tex]\frac{1problem}{1.5min} * \frac{60min}{1hr}[/tex]
After that, we want to know how many hours in a day:
[tex]\frac{1problem}{1.5min} * \frac{60min}{1hr} * \frac{24hr}{1d}[/tex]
and how many days in one week:
[tex]\frac{1problem}{1.5min} * \frac{60min}{1hr} * \frac{24hr}{1d} * \frac{7d}{1w}[/tex]
To solve the dimensional analysis problem, we multiply across the top of the entire expression, then divide across the bottom. So:
1 * 60 * 24 * 7 = 10,080
And then divide that by the bottom:
10,080 / 1.5 / 1 / 1 / 1 = 6,720
So you can solve 6,720 problems in one week. Multiply that by six and we get your answer:
40,320 dimensional analysis problems can be completed in 6 weeks of Chemistry class.
