Question 177692: Jack usually mows his lawn in 6 hours. Marilyn can mow the same yard in 7 hours. How much time would it take for them to mow the lawn together?
(simplify your answer. Type and integer, proper fraction, or mixed number)
Thank you in advance for your help
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! rate * time = units
units = 1 (the lawn)
jack can mow the lawn in 6 hours, so jack's rate is 1/6 per hour, because:
jack's rate * 6 = 1
jack's rate = 1/6
marilyn can mow the lawn in 7 hours, so marilyn's rate is 1/7 per hour, because:
marilyn's rate * 7 = 1
marilyn's rate = 1/7
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if they work together, then their rates are additive, so the equation of them working together is:
(1/6 + 1/7) * combined time = 1
multiply both sides of this equation by 42 since 42 = 6*7 and that will allow you to remove the denominators from the equation.
(42/6 + 42/7) * combined time = 42*1
which becomes:
7 + 6) * combined time = 42
which becomes:
13 * combined time = 42
divide both sides by 13 to get:
combined time = 42/13 hours = 3 + 3/13 hours
your answer is that they would take 3 hours + 3/13 of an hour to mow the lawn together.
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you can convert this to decimals by dividing 3/13 and adding it to 3 to get:
3.230769231 hours.
time in hours rounded to the nearest thousandths of an hour is:
3.231 hours.
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you can convert this to hours and minutes and seconds by doing the following:
3 and 3/13 hours
= 3 hours
+ 3/13 hours * 60 = 13.84615385 minutes
= 13 minutes
+ .84615385 minutes * 60 = 50.76923077 seconds
= 51 seconds rounded to the nearest second.
time in hours minutes seconds is:
3 hours 13 minutes 51 seconds
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you can prove the equation is good by substituting in the original combined equation.
(1/6 + 1/7) * 3.230769231 = 1
this becomes:
(7+6)/42)*3.230769231 = 1
which becomes:
13/42 * 3.230769231 = 1
which becomes:
1 = 1
proving the combined time is accurate.
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