If a light bulb that burns 3 hours a day lasts for 22.8 years, then how long will a light bulb that burns for 7 hours a day last?
(3/7)(22.8) =
burnhours of the lightbulb = 3(22.8) = 68.4
time for a bulb that burns 7 hours/day
= 68.4/7 =9.77
or 9.8 years
or
the time is inversely proportional to the rate
T = k/R
22.8 = k/3
k = 3(22.8) = 68.4
T = 67.4/R
= 67.4/7 = appr 9.8
Notice the calculations are the same
To find out how long a light bulb that burns for 7 hours a day will last, we can use the given information about the first light bulb that burns for 3 hours a day and lasts for 22.8 years.
First, let's calculate how many hours the first light bulb lasts in total:
Total hours the first light bulb lasts = hours burned per day * number of years
Total hours the first light bulb lasts = 3 hours/day * 365 days/year * 22.8 years
Now, we can use the total hours the first light bulb lasts to find out the lifespan of a light bulb that burns for 7 hours a day:
Lifespan of the second light bulb = Total hours the first light bulb lasts / hours burned per day of the second light bulb
Lifespan of the second light bulb = (3 hours/day * 365 days/year * 22.8 years) / 7 hours/day
To simplify the calculation, we can convert the years and days to hours:
Total hours the first light bulb lasts = 3 hours/day * 365 days/year * 22.8 years
Total hours the first light bulb lasts = 24,858 hours
Now we can substitute this value into the equation to find the lifespan of the second light bulb:
Lifespan of the second light bulb = 24,858 hours / 7 hours/day
Calculating this gives us the answer:
Lifespan of the second light bulb = 3540.86 days
Therefore, a light bulb that burns for 7 hours a day would last approximately 3540.86 days, or approximately 9.7 years.