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: $3+3\frac{1}{3}=3+\frac{10}{3}=\frac{19}{3}$

Why?

From the statement we know:

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

$\frac{3}{4}*4=\frac{12}{4}=3 gallons$

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

$\frac{5}{6}*4=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}gallons$

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:

$3+\frac{1}{3} =\frac{(3*3)+(1*1)}{3*1}=\frac{9+1}{3}=\frac{10}{3}$

Have a nice day!