SOLUTION: Hi. I need some help solving this problem please. Jack can mow the baseball grounds in 6 hours; Mike can mow the same grounds in 5 hours and Chris can mow the grounds in 4 hours

Algebra ->  Proportions -> SOLUTION: Hi. I need some help solving this problem please. Jack can mow the baseball grounds in 6 hours; Mike can mow the same grounds in 5 hours and Chris can mow the grounds in 4 hours      Log On


   

Question 845497: Hi. I need some help solving this problem please.
Jack can mow the baseball grounds in 6 hours; Mike can mow the same grounds in 5 hours and Chris can mow the grounds in 4 hours. How long will it take to mow the grounds if all 3 work together? (Leave the answer in improper fraction form)
This is what I came up with but i'm not too sure:
1/6 + 1/5 + 1/4 = 1/t(time)
10t + 12t + 15t= 37t
37t/37 = 60/37 t=60/37
Thanks in advance.



Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

1/6 + 1/5 + 1/4 = 1/t   Yes.  Good Work.

|Multiplying thru by +highlight_green%2860t%29 so as all denominators = 1

 10t + 12t + 15t = 60

    37t = 60

      t = 60/37 hrs

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jack can mow the baseball grounds in 6 hours
Jack rate = 1/6 job/hr
-------------------------------
Mike can mow the same grounds in 5 hours
Mike rate = 1/5 job/hr
-------------------------------
and Chris can mow the grounds in 4 hours.
Chris rate = 1/4 job/hr
-------------------------------
Together rate = 1/x job/hr
----------------------------------
Equation:
rate + rate + rate = together rate
[ 1/6 + 1/5 + 1/4] = 1/x
x[(5*4 + 6*4+ 6*5)/(6*5*4)] = 1
----
x(74/120) = 1
x = 120/74 = 1.62 hours = 1 hr 37 min 18 sec
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Note: Your answer is correct.
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