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Question 160276: One job. two power shovels excavate 20,000 cubic meters of earth, the larger shovel working for 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each move in 1 hour working alone?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! One job. two power shovels excavate 20,000 cubic meters of earth, the larger shovel working for 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each move in 1 hour working alone?
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Let x = large shovel amt of earth moved in 1 hr
Let y = small shovel amt in 1 hr
;
Write an equation for each project:
40x + 35y = 20000
70x + 90y = 40000
:
Simplify, divide the 1st equation by 5, and the 2nd equation by 10
8x + 7y = 4000
7x + 9y = 4000
:
Multiply the 1st equation by 7 and the 2nd equation by 8
56x + 49y = 28000
56x + 72y = 32000
----------------------subtraction eliminates x
0x - 23y = - 4000
y = 
y ~ 174 yds/hr, the small shovel
:
Find x using; 7x + 9y = 4000
7x + 9(174) = 4000
7x = 1566 = 4000
7x = 4000 - 1566
7x = 2434
x = 
x ~ 348 yds/hr, the large shovel
:
:
Check solution in 1st original equation:
40x + 35y = 20000
40(348) + 35(174) =
13920 + 6090 = 200010 ~ 20000
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