SOLUTION: 5 men and 4 women can shovel as much snow in 6 days as 4 men and 6 women can shovel in 5 days. Who are the better workers, the men or women and by how much?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 5 men and 4 women can shovel as much snow in 6 days as 4 men and 6 women can shovel in 5 days. Who are the better workers, the men or women and by how much?      Log On


   

Question 1065626: 5 men and 4 women can shovel as much snow in 6 days as 4 men and 6 women can shovel in 5 days. Who are the better workers, the men or women and by how much?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
R*T=W for rate, time, amount of work. The description does not specifically give the unit of work or the amount of snow.

If x is rate for 1 woman and y is rate for 1 man, then for the given described equal amount of work, "1 work" or "1 job",
system%28%285y%2B4x%29%2A6=1%2C%284y%2B6x%29%2A5=1%29

system%2824x%2B30y=1%2C30x%2B20y=1%29
Multiply the first of these by 2, and the second of these by 3, to eliminate y and find x, first.

system%2848x%2B60y=2%2C90x%2B60y=3%29
-
%2890x%2B60y%29-%2848x%2B60y%29=3-2
42x=1
highlight_green%28x=1%2F42%29------in whatever units of work per day.

30%281%2F42%29%2B20y=1
20y=1-30%2F42
20y=1-5%2F7
20y=2%2F7
y=2%2F%28140%29
highlight_green%28y=1%2F70%29------the rate for one man.

system%281%2F42%3E1%2F70%2Cx%3Ey%29
The women are the better workers.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
5 men and 4 women can shovel as much snow in 6 days as 4 men and 6 women can shovel in 5 days. Who are the better workers, the men or women and by how much?
I don't know about being "better" workers, but when it comes to time taken to do the shoveling, a man is faster, as a woman takes twice the time a man takes.

OR

In both cases, the men did a larger portion of the shoveling than the women.

In the 6 days taken to shovel, the 5 men did 5%2F7 of the shoveling, while the 4 women did 2%2F7.

In the 5 days taken to shovel, the 4 men did 4%2F7 of the shoveling, while the 6 women did 3%2F7.