Word problem, please help!?
When all the leaves have fallen, a girl can rake the entire yard in 8 hours. When a boy does it alone, it takes him 9 hours. How long would it take them to rake the yard together? Round to the nearest minute.
When all the leaves have fallen, a girl can rake the entire yard in 8 hours. When a boy does it alone, it takes him 9 hours. How long would it take them to rake the yard together? Round to the nearest minute.
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First, realize that it will be less than 8 hours. Since 8 is the faster person, any help at all results in less than 8. Also, it will be more than 4. If they both worked at same speed as the faster (8 hr) person then youd expect it to be done in half the time. (Half of 8 is 4). Ok so one person does in 8, so that person completes 1/8 of a yard in 1 hr. The other person completes 1/9 of the yard in 1 hr. Together they complete (1/8 + 1/9) yard in 1 hr. These add to (17/72) per hr. So it will take 1/(17/72) hours to finish. Which is 72/17 or 4 4/17 hours. Now for the quick formula: product over the sum: (8 × 9) / (8 + 9) = 72/17.
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In 1 hour: 1/8 and 1/9 is raked or 9/72+8/72=17/72, 72/17=4.23 hours, or 9/8=1.125 unit of speed for girl, 1 unit of speed for boy. 9/2.125= 4.23 hours
Mercy
1/8 + 1/9 = 72
9x + 8x = 72
17x = 72
x = 72/17 hr 0r 4 4/17 hr
Amy
How many yards could they rake in 72 hours?