Question

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own???

Answer 1

please help!! @Muzzack @RadEn @iPwnBunnies

Answer 2

(x + x- 8 )/x(x-8) = 3
solve for x

Answer 3

?

Answer 4

opsss, backward that should like
x(x-8)/(x+x-8) = 3

Answer 5

ok so cant we cancel some x's or no

Answer 6

with x is the Jimmy's time if he complete the job alone
x(x-8)/(x+x-8) = 3
(x^2 - 8x)/(2x-8) = 3
cross multiply then simplify and solve for x (notice that it must be positive)

Answer 7

\[\frac{ x ^{2}-8x }{ 2x-8 }=\frac{ 3 }{ 1 }\]

Answer 8

yes, just continue that ...

Answer 9

so x^2-8x/6x-24?

Answer 10

x^2-8x = 6x-24
simply by combine then solve for x

Answer 11

x^2-14x+24=0?

Then what

Answer 12

looks it can be factored :)
can you factorize the LHS ?

Answer 13

(x-12)(x-2)=0

Answer 14

yes, that's right. then set up each factor be equal zero then solve for x

Answer 15

x=12 and x=2? is that what you meant?

Answer 16

yep, but we have to recheck again which one of that numbers can be solution for this problem. see before i take by assumed x = jimmy's time and x-8 = harry's time if they do the job alone. now if you subtitute both value of x above, which one possible as the answer ?

if x = 2, then x - 8 = 2 - 8 = -6 (it cant)
if x = 12, then x-8 = 12-8 = 4 (nah, this is a positive number), so x = 12 is satisfies as the solution

Answer 17

ok so x=12 is the solution? :)

Answer 18

yep, because it would give us
Jimmy = 12
Harry = 4 (see that harry 8 hours faster than Jimmy)

Answer 19

ohhh thank you! :D

Answer 20

you're welcome :)