ellexay wrote:Here is the problem: J working alone can repair 2 sections of trail in r hrs. K working alone can repair 1 section in p hrs. How long will it take J & K to repair a trail 6 sections long if they work together?
ANS: 6rp/2p+r
HELP! Thank you!
One approach you can take to combined work problems is to calibrate each worker to the same amount of time. It's easier to understand the sequence of steps using a numerical example first:
Say Worker A can complete 2 jobs in 10 hours. How long to complete 1 job? 5 hours --> we divide by 2.
Say worker A can complete 2 jobs in 10 hours. How many jobs will he or she complete in 60 hours? Well, working six times as long, A will do six times the work: we multiply by 6, so A will complete 12 jobs.
We can do the same operations for the above question, though it's more abstract because of the presence of the letters. Still, at each stage, we are simply multiplying or dividing, just as we would do if we were working with numbers. Here, for example, we know:
J can complete 2 jobs in r hours
K can complete 2 job in 2p hours
We can now work out how many jobs they would each do in 2rp hours, by multiplying:
J can complete 4p jobs in 2rp hours
K can complete 2r jobs in 2rp hours
J+K together complete 4p + 2r jobs in 2rp hours
Now divide by 4p + 2r to see how long it takes to complete 1 job:
J+K together complete 1 job in 2rp/(4p + 2r) hours
And finally multiply by 6 to see how long it takes to complete 6 jobs:
J+K together complete 6 jobs in 12rp/(4p + 2r) = 6rp/(2p + r) hours
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The combined rate formula could likely also be used here if you know that formula, though if you do as above, you don't need it.
