Word Problem [2]

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DanieldeLucena

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Jul 29, 2010
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A dog chases a fox who is 60 jumps in front, while the fox gives 9 jumps the dog gives 6 jumps, but each 3 dog's jumps is equivalent to 7 fox's jumps. How many jumps should give the dog to reach the fox?
Resp.: 72 jumps
How can I get it ??? I swear I'm trying so hard ...

Very very thanks
 
Hello, DanieldeLucena!

Wow . . . This is a confusing problem!
. . There are dog-jumps and fox-jumps.
. . There are dog-speed and fox-speed.

A dog chases a fox who is 60 jumps in front.
. . I assume that the fox has a lead of 60 fox-jumps.
While the fox gives 9 jumps, the dog gives 6 jumps.
Each 3 dog's jumps is equivalent to 7 fox's jumps.

How many jumps should the dog make to reach the fox?

Answer: 72 jumps
Click to expand...

No time unit was given, so let's assume the following:

. . Fox-speed: .9 fox-jumps per minute.
. . Dog speed: .6 dog-jumps per minute.


\(\displaystyle 3\text{ dog-jumps} \:=\: 7\text{ fox-jumps} \quad\Rightarrow\quad 1\text{ dog-jump} \:=\:\tfrac{7}{3}\text{ fox-jumps}\)

\(\displaystyle \text{Hence: Dog-speed}\:=\:\text{6 dog-jumps per minute} \quad\Rightarrow\quad \tfrac{7}{3}\;\times\; 6 \:=\:14\text{ fox-jumps per minute}\)


\(\displaystyle \text{The difference of their speeds is: }\:14 - 9 \:=\:5\text{ fox-jumps per minute.}\)


\(\displaystyle \text{The fox has a headstart of 60 fox-jumps.}\)
\(\displaystyle \text{It will take the dog }\tfrac{60}{5} \:=\:12\text{ minutes to catch up.}\)

\(\displaystyle \text{In 12 minutes, the dog makes: }\:12 \times 6 \:=\:72\text{ dog-jumps.}\)


Is there a neater solution? . . . I hope so!
.
 
I'm assuming that the fox is 60 "dog" jumps ahead of the dog; otherwise, my brain fuses.

If 3 dog jumps cover the same distance as 7 fox jumps, then 6 dog jumps covers the same distance as 14 fox jumps.

Therefore, the dog gains 5 jumps for every 9 jumps of the fox (14 - 9 = 5).

Or, said another way, every time the dog jumps six times, the 60-jump distance is reduced by 5 jumps.

How many times will the dog need to jump six times, to reduce the 60-jump lead to zero?

60/5 = 12

12 times 6 jumps is the total number of jumps required.
 
Oh. It looks like maybe Soroban and I just showed that it doesn't matter if the lead units are dog jumps or fox jumps. We both came up with the same result, anyway.
 
That's really a confusing question, but you two are right ...
Man you're crazy ... You're very good ...

Thanks very much...
 
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