document.write( "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?
\n" ); document.write( "(simplify your answer. Type and integer, proper fraction, or mixed number)\r
\n" ); document.write( "\n" ); document.write( "Thank you in advance for your help \n" ); document.write( "
Algebra.Com's Answer #132708 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
rate * time = units
\n" ); document.write( "units = 1 (the lawn)
\n" ); document.write( "jack can mow the lawn in 6 hours, so jack's rate is 1/6 per hour, because:
\n" ); document.write( "jack's rate * 6 = 1
\n" ); document.write( "jack's rate = 1/6
\n" ); document.write( "marilyn can mow the lawn in 7 hours, so marilyn's rate is 1/7 per hour, because:
\n" ); document.write( "marilyn's rate * 7 = 1
\n" ); document.write( "marilyn's rate = 1/7
\n" ); document.write( "---
\n" ); document.write( "if they work together, then their rates are additive, so the equation of them working together is:
\n" ); document.write( "(1/6 + 1/7) * combined time = 1
\n" ); document.write( "multiply both sides of this equation by 42 since 42 = 6*7 and that will allow you to remove the denominators from the equation.
\n" ); document.write( "(42/6 + 42/7) * combined time = 42*1
\n" ); document.write( "which becomes:
\n" ); document.write( "7 + 6) * combined time = 42
\n" ); document.write( "which becomes:
\n" ); document.write( "13 * combined time = 42
\n" ); document.write( "divide both sides by 13 to get:
\n" ); document.write( "combined time = 42/13 hours = 3 + 3/13 hours
\n" ); document.write( "your answer is that they would take 3 hours + 3/13 of an hour to mow the lawn together.
\n" ); document.write( "---
\n" ); document.write( "you can convert this to decimals by dividing 3/13 and adding it to 3 to get:
\n" ); document.write( "3.230769231 hours.
\n" ); document.write( "time in hours rounded to the nearest thousandths of an hour is:
\n" ); document.write( "3.231 hours.
\n" ); document.write( "---
\n" ); document.write( "you can convert this to hours and minutes and seconds by doing the following:
\n" ); document.write( "3 and 3/13 hours
\n" ); document.write( "= 3 hours
\n" ); document.write( "+ 3/13 hours * 60 = 13.84615385 minutes
\n" ); document.write( "= 13 minutes
\n" ); document.write( "+ .84615385 minutes * 60 = 50.76923077 seconds
\n" ); document.write( "= 51 seconds rounded to the nearest second.
\n" ); document.write( "time in hours minutes seconds is:
\n" ); document.write( "3 hours 13 minutes 51 seconds
\n" ); document.write( "---
\n" ); document.write( "you can prove the equation is good by substituting in the original combined equation.
\n" ); document.write( "(1/6 + 1/7) * 3.230769231 = 1
\n" ); document.write( "this becomes:
\n" ); document.write( "(7+6)/42)*3.230769231 = 1
\n" ); document.write( "which becomes:
\n" ); document.write( "13/42 * 3.230769231 = 1
\n" ); document.write( "which becomes:
\n" ); document.write( "1 = 1
\n" ); document.write( "proving the combined time is accurate.
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