Question

Two employees are painting a boat. One uses ¾ gallon of paint each hour, one uses 1 ⅔ gallon of paint every 2 hours. How much paint will they use in 4 hours?

Answer 1

Hello!

The answer is:

First employee: 3 gallons

Second employee: 3 1/3 gallons

Total:
`3+3(1)/(3)=3+(10)/(3)=(19)/(3)`

Why?

From the statement we know:

First employee uses 3/4 gallon each our, for 4 hours the will use:

`(3)/(4)*4=(12)/(4)=3 gallons`

Second employee uses 1 2/3 (5/3) gallon every 2 hours, meaning 5/6 gallon each hour.

`(5)/(6)*4=(20)/(6)=(10)/(3)=3(1)/(3)gallons`

Remember, to sum (algebraic sum) fractions we should follow the next steps:

First: Multiply both fractions denominators by each other in order to get the denominator of the new fraction.

Second: Multiply the numerator of the first fraction by the denominator of the second fraction.

Third: Multiply the denominator of the first fraction by the denominator of the second fraction.

Fourth: Sum (algebraic sum) each result and divide it into the number obtained from the first step (denominator of the new fraction).

Example:

`3+(1)/(3) =((3*3)+(1*1))/(3*1)=(9+1)/(3)=(10)/(3)`

Have a nice day!