Question 177692
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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