proportional problem

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ual_1

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May 1, 2012
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Jill, Apple and Peter each planted a tree 90 cm in height. In the time it took Jill's tree to grow 1 cm, Apple's tree grew 2 cm. In the time it took Apple's tree to grow 1 cm, Peter's tree grew 3 cm. The question is: How tall was Jill's tree when Peter's tree was 108 cm in height? There is four possible answers: 18cm, 36cm, 93cm or 96cm.

Please help with your explanation, thanks.
ual_1
 
ual_1 said:
Jill, Apple and Peter each planted a tree 90 cm in height. In the time it took Jill's tree to grow 1 cm, Apple's tree grew 2 cm. In the time it took Apple's tree to grow 1 cm, Peter's tree grew 3 cm. The question is: How tall was Jill's tree when Peter's tree was 108 cm in height? There is four possible answers: 18cm, 36cm, 93cm or 96cm.

Please help with your explanation, thanks.
ual_1
Click to expand...

Let's try to dissect the information you've been given. How many times faster does Peter's tree grow than Apple's? It says when Apple's tree grows 1cm, Peter's grows 3cm. So it grows three times faster. Similarly, Apple's tree grows 2cm for every 1cm that Jill's tree grows. That is, it grows two times faster.

So how much faster does Peter's grow than Jill's?
 
it's 3 x 2 = Peter is 6 times faster than Jill. then the height of Jill's tree should be 108cm divide 6 = 18cm.
However, the arguable answer is 93cm not 18cm. It's a bit hard to figure it out why 93cm is the answer, pls input your comments. Thanks.
 
ual_1 said:
it's 3 x 2 = Peter is 6 times faster than Jill. then the height of Jill's tree should be 108cm divide 6 = 18cm.
However, the arguable answer is 93cm not 18cm. It's a bit hard to figure it out why 93cm is the answer, pls input your comments. Thanks.
Click to expand...

Ah, you need to read more carefully! If they had started at a height of ZERO you would be correct. They didn't though, did they?
 
Yes, they planted the tree in height 90cm already. So, when they started after 90cm each and Peter is 6 times faster than Jill, then Jill's tree is 93cm (i/o 18cm) while Peter's tree is 108cm.
Thanks.
ual_1:D
 
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