Jan 11, 2010
RAY: Robert Underwood sent in the germ for this puzzler and I turned it into a full-fledged pandemic.
A few months ago Tommy, who in these last few years has become an avid gardener, harvested a bumper crop of juicy, ripe tomatoes. And this year, instead of making his usual 11 gallons of marinara sauce, he decided to try something a little different-sundried tomatoes.
Now, being the scientific type that he is, he decided to weigh his harvest at the outset and then again when he figured they had been sun dried enough. So Tom got the biggest cardboard box he could find. We stripped him down to his skivvies -- he didn't want to risk exceeding the weight limit of the scale -- and he and the box got on and weighed in at 148 pounds.
I then proceeded to begin filling the box to capacity. When no more tomatoes would fit I balanced one or two on his head, stuck a few under each armpit and wedged a couple between hisÂ… knees. Anyway, when they were all accounted for, the scale read 248 pounds. He had harvested exactly 100 pounds of tomatoes.
Now, in case you didn't know it, tomatoes are 99% water and 1% tomato stuff, you know like skin, seed casings, red dye no. 2, whatever is in tomatoes. But 99% of a tomato is water. So Tommy's 100 pounds of tomatoes are 99 pounds of H2O and 1 pound of whatever that other stuff is.
After a week in the sun drying out, Tommy's tomatoes were now 98% water. If we reweighed them and Tommy, like we had done a week earlier, what would the scale read?
A few months ago Tommy, who in these last few years has become an avid gardener, harvested a bumper crop of juicy, ripe tomatoes. And this year, instead of making his usual 11 gallons of marinara sauce, he decided to try something a little different-sundried tomatoes.
Now, being the scientific type that he is, he decided to weigh his harvest at the outset and then again when he figured they had been sun dried enough. So Tom got the biggest cardboard box he could find. We stripped him down to his skivvies -- he didn't want to risk exceeding the weight limit of the scale -- and he and the box got on and weighed in at 148 pounds.
I then proceeded to begin filling the box to capacity. When no more tomatoes would fit I balanced one or two on his head, stuck a few under each armpit and wedged a couple between hisÂ… knees. Anyway, when they were all accounted for, the scale read 248 pounds. He had harvested exactly 100 pounds of tomatoes.
Now, in case you didn't know it, tomatoes are 99% water and 1% tomato stuff, you know like skin, seed casings, red dye no. 2, whatever is in tomatoes. But 99% of a tomato is water. So Tommy's 100 pounds of tomatoes are 99 pounds of H2O and 1 pound of whatever that other stuff is.
After a week in the sun drying out, Tommy's tomatoes were now 98% water. If we reweighed them and Tommy, like we had done a week earlier, what would the scale read?
Answer:
RAY: Here's the answer. At the outset we had a hundred pounds of tomatoes. And we said they're 99% water and 1% whatever other solids there are. So, the solids were one pound.
TOM: Yeah.
RAY: And that one pound is not going to change when they dry out, it's still going to be one pound of solids. So, when the moisture content has been reduced to 98%, that mass of mushy, disgusting tomatoes is now two percent solids and 98% water. Right?
TOM: Yeah.
RAY: OK. Som we can write a very simple algebraic expression that says, two percent of X, where X is the total weight of the partially dried mess of tomatoes, has got to equal one pound. So .02 of X is one pound. And X is 50 pounds. When we put Tommy and these mushy tomatoes back on the scale, the scale's going to read 198 pounds. That's kind of hard to believe, that the moisture content goes from 99% to 98%, and the weight goes from 100 pounds down to 50.
TOM: Wow!
RAY: Let's not forget that when that mess of tomatoes is down to two pounds it's still 50% water.
TOM: Wow.
RAY: Pretty cute, eh? Do we have a winner?
TOM: We do have a winner, and the winner this week is Bruce Swanson from Hudson, Iowa. And for having his answer selected at random from among all the correct answers that we got, Bruce is going to get a $26 gift certificate to the Shameless Commerce Division of cartalk.com.
RAY: And what can you get with that, Johnny?
TOM: Absolutely nothing of value of course. But he can get a copy of our new CD, Tales of the Brothers Grime.
RAY: Ah yes, this is a new collection of stories that we've told on the air, including tales of my brother's misadventures in the United States Army.
TOM: Congratulations, Bruce!
TOM: Yeah.
RAY: And that one pound is not going to change when they dry out, it's still going to be one pound of solids. So, when the moisture content has been reduced to 98%, that mass of mushy, disgusting tomatoes is now two percent solids and 98% water. Right?
TOM: Yeah.
RAY: OK. Som we can write a very simple algebraic expression that says, two percent of X, where X is the total weight of the partially dried mess of tomatoes, has got to equal one pound. So .02 of X is one pound. And X is 50 pounds. When we put Tommy and these mushy tomatoes back on the scale, the scale's going to read 198 pounds. That's kind of hard to believe, that the moisture content goes from 99% to 98%, and the weight goes from 100 pounds down to 50.
TOM: Wow!
RAY: Let's not forget that when that mess of tomatoes is down to two pounds it's still 50% water.
TOM: Wow.
RAY: Pretty cute, eh? Do we have a winner?
TOM: We do have a winner, and the winner this week is Bruce Swanson from Hudson, Iowa. And for having his answer selected at random from among all the correct answers that we got, Bruce is going to get a $26 gift certificate to the Shameless Commerce Division of cartalk.com.
RAY: And what can you get with that, Johnny?
TOM: Absolutely nothing of value of course. But he can get a copy of our new CD, Tales of the Brothers Grime.
RAY: Ah yes, this is a new collection of stories that we've told on the air, including tales of my brother's misadventures in the United States Army.
TOM: Congratulations, Bruce!
