Question

Frankie can plant a garden by herself in 10 hours. when her son Garyn helps her, the total time it takes them to plant the garden is 4 hours. how long would it take Garyn to plant the garden himself?

Answer 1

`6(2)/(3)\ hours`

Explanation:

step 1

we know that

Frankie can plant a garden by herself in 10 hours

so

100% of the work -------> 10 hours

Using proportion

Find the percentage he can do in 1 hour

`(100\%)/(10)=(x\%)/(1) \\ \\x=100/10\\ \\x=10\%`

step 2

we know that

When her son Garyn helps her, the total time it takes them to plant the garden is 4 hours

so

100% of the work (Frankie and Garyn) -------> 4 hours

Remember that

Frankie in 1 hour can do 10%

so

Frankie in 4 hours can do----------> 10%*4=40%

therefore

Garyn in 4 hours can do--------> 100%-40%=60%

step 3

using proportion

Find how long would it take Garyn to plant the garden himself

`(60\%)/(4) =(100\%)/(x)\\ \\x=4*100/60\\ \\x= 6(2)/(3)\ hours`