Question 1013216: In a basket factory,lan finished 5 baskets in 2 hours while joy finished 10 baskets in 3 hours. If they work at the same rate, how many baskets can they finish together in 12 hours?
Please help,cause i dont understand! my mom gonna suspend me help me. with solution pleaseeeeee
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula to use is rate * time = quantity of work produced.
rate is the quantity of work produced per unit of time.
time is the amount of time taken to finish the work.
this formula means:
if you produce r units of work per unit of time and you work for t units of time, then you will produce q amount of work.
for example:
if i can finish 3 baskets per hour and i work for 3 hours, then i will finish 9 baskets in those 3 hours.
in this problem, you are given that ian can finish 5 baskets in 2 hours.
the rate * time formula for him becomes:
r * 2 = 5
r is the number of baskets he can produce per hour.
2 is the time in hours it took to finish the basket.
5 is the number of baskets.
since you know time and quantity, you can solve for the rate.
start with r * 2 = 5
divide both sides of the equation by 2 to get r = 5/2.
ian's rate is finishing 5/2 baskets per hour.
that's the same as 2.5 baskets per hour because 5/2 = 2.5.
joy finished 10 basket in 3 hours.
the rate * time = quantity of work produce formula for her would be:
r * 3 = 10
solve for r to get r = 10/3.
joy's rate is finishing 10/3 baskets per hour.
that's the same as 3.333... because 10/3 = 3.333...
when they work together, their rates are additive.
ian's rate is 5/2 baskets per hour.
joy's rate is 10/3 baskets per hour.
add these rates together and you get 5/2 + 10/3.
if you multiply 5/2 by 3/3 you get 15/6.
ifyou multiply 10/3 by 2/2 you get 20/6.
now that you have common denominators, you can add them together.
5/2 + 10/3 = 15/6 + 20/6 = 35/6.
their combined rate when they work together is 35/6 baskets per hour.
the decimal equivalent of that is 5.833... baskets per hour.
the same rate * time formula is used only now you are using their combined rate rather than each individual's rate.
r * t = q
r is the combined rate of 35/6 baskets per hour.
t is the time in hours which is equal to 12.
q is the number of baskets produced which remains at q because we don't know that is is just yet.
their combined formula becomes:
35/6 * 12 = q
solve this equation for q and you get q = 70 baskets.
when they worked together for 12 hours at at their combined rate of 35/6 baskets per hour, they finished 70 baskets.
first you had to solve for the rate of each.
then you had to add their rates together.
then you had to apply that combine rate in the final equation.
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