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Lena [83]
2 years ago
10

At noon the minute and the hour hands overlap. In how man hours and minutes will it happen next?

Mathematics
2 answers:
Over [174]2 years ago
8 0
1:05, once 12:00 (noon) has changed to 1:00 (the short hand at 1 and the long hand at 12) the long hand will soon shift over to the 1 indicating its 1:05
Readme [11.4K]2 years ago
7 0

It would happen again at 1 hour and 5 minutes .

That is because at noon it is 12 p.m. and for the minute and the hour hands overlap, the next time it would happen is at 1:05 which is going to overlap again

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How many gallons of a 80% antifreeze solution must be mixed with 80 gallons of 15% antifreeze to get a mixture that is 70% antif
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440 gallons of 80 % antifreeze solution must be mixed with 80 gallons of 15% antifreeze to get a mixture that is 70% antifreeze

<em><u>Solution:</u></em>

Let "x" be the gallons of 80 % antifreeze added

Therefore, "x" gallons of 80 % antifreeze solution must be mixed with 80 gallons of 15% antifreeze

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"x" gallons of 80 % antifreeze solution must be mixed with 80 gallons of 15% antifreeze to get (x + 80) gallons of 70 % antifreeze

Thus, we get,

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x \times \frac{80}{100} + 80 \times \frac{15}{100} = (x+80) \times \frac{70}{100}\\\\0.8x + 80 \times 0.15 = (x+80) \times 0.7\\\\0.8x+12 = 0.7x+56\\\\0.8x-0.7x=56-12\\\\0.1x = 44\\\\x = \frac{44}{0.1}\\\\x = 440

Thus 440 gallons of 80 % antifreeze solution must be mixed

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