Name: Josh
level: secondary
student

1. A dog and a rabbit are 160 meters a part for every 9 meters that the dog runs , the rabbit jumps 7 meters. How many meters must the dog run in order to vertake the rabbit???

2. A cars odometer reads 15951 KM. Find the least number of kilomaters to travel until the palindromic number appears???

any help would be greatly apprectiated!!!! thanks in advance

Hi Josh,

The dog must make up the distance between them (160 meters). Since every time the dog runs 9 meters the rabbit jumps 7 meters, the dog only gains 2 meters on the rabbit for every nine he runs.

You could make a chart as follows to plot the progress:

Dog runs
9 meters
Rabbit jumps
7 meters
Gain by dog
2 meters
Distance between them
158 meters
18144156
27216154
etc.

You could continue on in this fashion and, although tedious, you would eventually come up with the right answer.

Now, an easier method uses proportions. By using proportional reasoning we can calculate how far the dog has to run to gain 160 meters:

```      2 meters gained   160 meters gained
--------------- = -----------------
9 meters run       ?? meters run
```

Now you simply cross multiply and divide to solve for ??

Your second question deals with palindromic numbers (numbers that are the same forwards and backwards).

The odometer reads 15951 now and you want to find how many kilometers from now the next palindromic number will occur. Since we have a five digit number, let's consider the first digit as fixed since I'm pretty sure palindromes will occur before the ten thousands digit changes to a two.

So we know we need the last digit to be 1.

Do we want the tens digit to be a five? By examining the last three digits we see that the next time the last two digits read " 51 " , the hundreds digit will have changed to a zero and the thousands digit will have changed to a six. " 51 " is no longer the desired last two digits.

Can you tell now what the next palindromic number will be?

Hope this helps.

Leeanne

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