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Potatoes are made up of 99% water and 1% “potato matter.”
Jack bought 100 pounds of potatoes and left them outside in
the sun for a while. When he returned, he discovered that
the potatoes had dehydrated and were now only made up of 98%
water. How much did the potatoes now weigh?
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Answer Posted / kerren (ko)
Okay so Kart had the right answer, I just want to explain it a little differently :)!!
Let's define: m = m_{water} + m_{potato}
Then m = 0.01*V*rho_{water} + 0.99*V*rho_{potato}
Where V is the volume of the potatoes and the rhos are the densities of the potato content and water.
The mass of the potato does not change (only the mass of the water) so m_{potato} remains constant!
The next day the new mass can be defined as:
m' = m_{water}' + m_{potato}'
BUT remember m_{potato} remains constant so m_{potato}' = m_{potato}
m' = 0.98*V'*rho_{water} + 0.02*V'*rho_{potato}
So we now know that the mass of the potato before is equal to the mass of the potato after, therefore:
0.01*V*rho_{potato} = 0.02*V'*rho_{potato}
Which leads to:
V'/V = (0.01*rho_{potato})/(0.02*rho_{potato})
So
V'/V = 0.5
And the ratio of mass will be the same as the ratios of volume:
V'/V = m'/m = 0.5
Therefore:
m'/100lb = 0.5
m' = 50lb
| Is This Answer Correct ? | 6 Yes | 2 No |
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