### Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

### Temperature

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

### Air Nets

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

# Food Chains

##### Stage: 3 Challenge Level:

Fast solutions:

a.

15000 caterpillars,

1500 birds

500 tigers.

b. They are getting $\frac{42}{75}$ = 56 % of what could get.

c. 10000 caterpillars = 1000 birds = 333 tigers, 267 tigers would starve.

d. 89286 tigers

Detailed solutions:

a.  The ratio is 1 bush : 30 caterpillars : 3 birds : 1 tiger, so with 500 bushes,

500 x 30 = 15000 caterpillars,

500 x 3 = 1500 birds,

500 x 1 = 500 tigers.

b. Lets say one bush contains 100 energy points. Then the caterpillars eat it, and have 75 points available to them. The birds get 75% of these points, 56 points, so the tiger has 42 points available to it. From eating the bush it could have obtained 75 points, so it's obtaining 42/75 = 56 % of what it could get.

c. We still have 500 bushes but now we have 10000 caterpillars, so

10000 x 10 = 1000 birds

10000/30 = 333 tigers

The new numbers would be the equilibrium point, 267 tigers would starve.

d.   500 bushes give 500 x 100 x 75 energy points. Tigers need 42 energy points, so the tiger population would increase to $\frac{500 \times 100 \times 75}{42}$ = 89286 tigers!

The caterpillar and bird populations would be left with no food and would decrease unless they found another source of food.