SOLUTION: John takes 3 hours longer than Andrew to
peel 500 pounds (lb) of apples. If together they can peel
500 lb of apples in 8 hours, then how long would it take
each one working alon
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-> SOLUTION: John takes 3 hours longer than Andrew to
peel 500 pounds (lb) of apples. If together they can peel
500 lb of apples in 8 hours, then how long would it take
each one working alon
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Question 327804: John takes 3 hours longer than Andrew to
peel 500 pounds (lb) of apples. If together they can peel
500 lb of apples in 8 hours, then how long would it take
each one working alone Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! John takes 3 hours longer than Andrew to peel 500 pounds (lb) of apples.
If together they can peel 500 lb of apples in 8 hours, then how long would it
take each one working alone.
:
Let t = time required by Andrew
then
(t+3) = time required by John
:
Let the completed job = 1; (the peeling of 500 lb of potatoes)
:
Each person will do a fraction of job, the two fractions add up to 1 + = 1
Multiply by t(t+3),
results:
8(t+3) + 8t = t(t+3)
:
8t + 24 + 8t = t^2 + 3t
:
16t + 24 = t^2 + 3t
Arrange as quadratic equation
t^2 + 3t - 16t - 24 = 0
:
t^2 - 13t - 24 = 0
Use the quadratic formula to find t
x=t, a=1, b=-13, c=-24
:
:
The positive solution is what we want here:
t =
t = 14.64 hrs, Andrew working alone
then
14.64+3 = 17.64 hrs, John working alone
:
:
Check solution + =
.546 + .454 = 1
You can put this solution on YOUR website! John takes 3 hours longer than Andrew to
peel 500 pounds (lb) of apples. If together they can peel
500 lb of apples in 8 hours, then how long would it take
each one working alone
This is a slightly different approach. The other tutor added
up fractions of a job in one hour. I take it from a rate
approach, whene their rate together equals the sum of their
individual rates. Either way is correct. I just prefer this
method.
Make this chart
Number of Time Rate
batches of in in
apples hours batches/hr
-------------------------------------------------
John alone
Andrew alone
Both together
Let Andrew's time working alone be x. We fill that in:
Number of Time Rate
batches of in in
apples hours batches/hr
-------------------------------------------------
John alone
Andrew alone x
Both together
>>...John takes 3 hours longer than Andrew...<<
So John's time working alone is x+3, so we fill that in.
Number of Time Rate
batches of in in
apples hours batches/hr
-------------------------------------------------
John alone x+3
Andrew alone x
Both together
>>...together they can peel 500 lb of apples in 8 hours...<<
So we fill that in for the time for both together:
Number of Time Rate
batches of in in
apples hours batches/hr
-------------------------------------------------
John alone x+3
Andrew alone x
Both together 8
In all three cases exactly 1 batch (500 lbs) of apples are peeled.
So we put 1's for the number of batches of apples peeled.
Number of Time Rate
batches of in in
apples hours batches/hr
-------------------------------------------------
John alone 1 x+3
Andrew alone 1 x
Both together 1 8
Now we form the three rates by Rate =
Number of Time Rate
batches of in in
apples hours batches/hr
-------------------------------------------------
John alone 1 x+3 1/(x+3)
Andrew alone 1 x 1/x
Both together 1 8 1/8
Now we make the equation by:
John's alone rate + Andrew's rate alone = Rate of both together
1/(x+3) + 1/x = 1/8
Can you solve that by first getting the LCD? If not post again asking how.
Solution: .
Those two solutions are approximately
and
We ignore the negative answer and conclude that Andrew's time
alone is about 14.6 hours and since John takes 3 hours longer,
or about 14.6 + 3 = 17.6 hours.
Edwin
