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A
friend of mine just send me an email asking some help to solve some algebra, related to "Work problems" (though, she didn't mentioned what these algebra problems for I still managed to respond to her). I paused for a while and re-calibrate myself to grasp the problems and send some solutions to her. I know, this is a bit silly on my part as most of the primary schools already teaching the students on this type of algebra problems. This seems I'm in the contest of "Are You Smarter Than a 5th Grader" TV shows!

Anyway, here are the problems:

1. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

Solution:
Let the "x" be the distance that both cyclists will meet( where second cyclist will catch-up the first cyclist.

x = 10T -> equation 1; x = 6(T + 3) -> equation 2
10T = 6(T+3)
10T = 6T + 18
4T = 18
T=4.5hrs

2. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

Solution:
Determine how fast(rate) each person to complete the 20 drinks.
Steven = 20/5 drinks/minute
Sue = 20/10 drinks/minute
Jack = 20/15 drinks/minute

Therefore, the time (in T) to complete the 20 drinks if Steven, Sue & Jack together is:
20/T = 20/5 + 20/10 + 20/15
20/T = 4 + 2 + 4/3
20/T = 6 + 4/3
20/T = (18+4)/3
20/T = 22/3
T = 2.72 minutes
T = 2 minutes and 43.6 seconds

3. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?

Solution:
Same approach on the preceeding item. Let “x” represents the job to complete.

Sam = x/4
Lisa = x/6
Tom = x/2

x/T = x/4 + x/6 + x/2
(x/T = x/4 + x/6 + x/2) /x -> divide x

1/T = ¼ + 1/6 + ½
1/T = (3 + 2 + 6)/12
1/T = 11/12
T = 12/11
T = 1.09 days