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Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

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Lower Bound

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

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Sum Equals Product

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?

Tyre Wear

Stage: 3 Short Challenge Level: Challenge Level:1
Of the $5$ tyres, $4$ are used at any one time, so each tyre is used for $\frac{4}{5}$ of the journey, or $$\frac{4}{5} \times 30000 \; \text{km} = 24000 \; \text{km}$$

This problem is taken from the UKMT Mathematical Challenges.