Question 1206703: Allen can do a job 5 times faster than Billy. Billy can do the same job in 8 hours. How long will it take to do it together?
Found 4 solutions by josgarithmetic, greenestamps, Edwin McCravy, math_tutor2020:
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! "5 times faster than..."
RATE TIME JOB
Allen 1/8+5(1/8) 1
Billy 1/8 8 1
Description relates to just doing 1 job. The two people working together do so at the sum of the individual rates.
 , jobs per hour.
 ---------their combned rate of work, as jobs per hour.
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
A math problem should never be written using any phrase like "... 5 times faster than..." or "... 4 times older than..." or "... 3 times more than...".
Almost certainly, the intended information is that Allen does the job "5 times AS FAST AS" Billy. In that case, Allen is like 5 Billys, so it's as if 6 Billys are working on the job. 6 Billys will take 1/6 as long as one Billy, so the time it would take to do the job together is 1/6 of 8 hours, or 4/3 hours, or 1 hour and 20 minutes.
However, with the given information that Allen can do the job 5 times FASTER THAN Billy, the conclusion must be that Allen's rate of work is 5 times FASTER THAN Billy's, which would mean that Allen is like one Billy PLUS 5 MORE Billys -- i.e., 1+5 = 6 Billys. In that case, working together would be like 7 Billys working together, in which case the time required to do the job together would be 1/7 of 8 hours, or 8/7 hours.
Unfortunately, in everyday sloppy English, "3 times more than" and "3 times as much as" are used to mean the same thing; grammatically, they do not. For the three examples of similar phrases in the first sentence of my response...
5 times FASTER THAN means 1+5=6 times AS FAST AS;
4 times OLDER THAN means 1+4=5 times AS OLD AS;
3 times MORE THAN means 1+3=5 times AS MUCH.
The difference in meaning between "3 times as much as" and "3 times more than" can be seen if we talk in percentages.
Suppose some measurement last year was x. Then...
If this year the measurement is 3 times AS MUCH AS last year, then it is 300% of what it was last year; the measurement now is 3x.
But if this year the measurement is 3 times MORE THAN last year, then it has GROWN BY 300%, which makes the measurement now x+3x = 4x.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! Allen can do a job 5 times faster than Billy.
Billy can do the same job in 8 hours.
How long will it take to do it together?
Here's the LCM method:
The LCM of the given numbers 5 and 8 is 40. Billy can do the same job in 8 hours.So Billy can do 5 jobs in 40 hours. Allen can do a job 5 times faster than Billy.So Allen can do 25 jobs in 40 hours.
So together they can do 30 jobs in 40 hours.
So together they can do 1 job in 40/30 hours,
or 1 1/3 hours or 1 hour and 20 minutes.
Edwin
Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!
Let's say the job is to move 80 boxes.
Billy can do the job in 8 hours when working alone.
His unit rate is 80/8 = 10 boxes per hour.
rate = amountDone/time
When Allen works alone, his rate is 5 times faster, so it is 5*10 = 50 boxes per hour.
Combined rate = 10+50 = 60 boxes per hour assuming neither person slows down the other.
rate*time = amountDone
time = amountDone/rate
time = 80/60 of an hour
time = 4/3 of an hour
time = 1 & 1/3 of an hour
time = 1 hour + 20 minutes
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