Question 817740: If mary can drink a whole bottle of wine in 2 hours, and her friend jessica can drink a whole bottle of wine in 3 hours. How long will it take them to drink one bottle of wine together.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mary can drink a whole bottle of wine in 2 hours.
jessica can drink a whole bottle of wine in 3 hours.
the rate that mary drinks a bottle of wine is equal to 1 bottle divided by 2 hours which is equal to 1/2. this means that mary drinks a half a bottle of wine per hour.
the rate that jessica drinks a bottle of wine is equal to 1 bottle divided by 3 hours which is equal to 1/3. this means that jessica drinks a third of a bottle of wine per hour.
obviously, mary drinks faster than jessica.
she can drink a half a bottle an hour while jessica can only drink a third of a bottle an hour.
when they drink together, their rates are additive.
this means that jessica and mary have a combined rate of 1/2 + 1/3 of a bottle per hour.
when you add 1/2 and 1/3 you need to get a common denominator so you multiply 1/2 by 3/3 and you multiply 1/3 by 2/2 and you get 3/6 + 2/6 which is equal to 5/6.
the combined rate of mary and jessica is therefore equal to 5/6 of a bottle per hour.
how long does it take them to drink a bottle together?
the formula is rate * time = units produced or consumed.
in this case, the rate is equal to 5/6 bottles per hour.
the time is what we want to find.
the units produced or consumed is equal to 1 bottle of wine.
the formula becomes
5/6 of a bottle consumed per hour * number of hours = 1 bottle of wine consumed.
algebraically, this is shown as:
5/6 * T = 1
this is derived from the formula R * T = Q, where R is equal to 5/6 and Q is equal to 1.
since only unknown, then you have to solve for T.
5/6 * T = 1 is the equation.
multiply both sides of this equation by 6/5 and you get:
6/5 * 5/6 * T = 6/5 * 1
simplify to get:
T = 6/5
it will take mary and jessica 6/5 of an hour to consume 1 bottle of wine when they drink from the same bottle together.
6/5 of an hours is equal to 1 hour and 1/5 of another hour which is equal to 1 hour and 1/5 * 60 minutes which is equal to one hour and 12 minutes.
let's look at the contribution of mary and jessica to the consumption of the bottle of wine.
we go back to the same equation of R * T = Q
mary consumes a bottle of wine at the rate of 1/2 bottle per hour.
the time is 6/5 of an hour.
her contribution is 1/2 * 6/5 = 3/5 of the bottle consumed in 6/5 of an hour.
jessica consumes a bottle of wine at the rate of 1/3 bottle per hour.
the time is 6/5 of an hour.
her contribution is 1/3 * 6/5 = 6/15 of the bottle which simplifies to 2/5 of the bottle.
in 6/5 of an hour, mary consumes 3/5 and jessica consumes 2/5 of the bottle.
add up their individual contributions to the consumption of the bottle and you see that the whole bottle has been consumed in 6/5 of an hour.
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