Question

one roofer can put a new roof on a house three times faster than another. working together, they can roof a house in 4 days. how long would it take the faster roofer working alone?
it seems so simple but for the life of me i cant figure it out, please help

Answer 1

roofer A is 3 times fatster than roofer B
A = 3B
A + B = a roof in 4 days
substitute B for 3A

A + 3A = 4 days
4 A = 4 days

it woud take 4 times as long, so 16 days?

im not sure at all though!

Answer 2

no israrani, that is incorrect.

Answer 3

it should be a+a/3 in 4 days, not a + 3a in 4 days

Answer 4

oh my bad! just found this site on stumbleupon and thought ild try one really quick haha sorry!

Answer 5

sophie, are you still interested in the answer or no?

Answer 6

one roofer can put a new roof on a house three times faster than another. Working together, they can roof a house in 4 days. How long would it take the faster roofer working alone?

Let x be the fastest roofers time to roof the house

Then the slower roofers time will be 3x

Use the following formula to calculate how the work is done:

\[\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\] where A & B are the times done by themselves, and C is the time it takes them to do the work together, thus we have:

\[\frac{1}{x}+\frac{1}{3x}+\frac{1}{4}\]\[\frac{4}{3x}=\frac{1}{4}\]\[3x=16\]\[x=\frac{16}{3}\]So the fast roofer can do it by himself in about 5.33 days!

Answer 7

\[100/4 = 25\] How much roof is laid in one day (%)
\[25/4 = 6.25\] How much roof is laid by the useless roofer (%)
\[6.25 * 3=18.75\] How much roof is laid by the godlike roofer (%)
\[100/18.75= \] how many days (roughly 5.33)

Answer 8

yes definitly intrested in the answer

Answer 9

well, sophie, nancy has given the answer in a nice form.

Answer 10

yes she has..thank you very much!!

Answer 11

click good answer if u like my answer,ty