Elizabeth was in the rain, moving at a speed of 40 km/hr. She noticed that the training moving towards them passed in 3 seconds. Find the speed of the other train if its length is 75 meters.

 Prove that if a+b is divisible by 3, then a³ + b³ is divisible by 9.

 p>0, q>0, pᐧq = 1.

Prove that

(1+1/p)(1+1/q)≥4

 Find the smallest natural number for which the sum of the cubes of its digits is not divisible by the sum of its digits.

 Jacob's home and school are both on the riverside. Jacob and the ship are starting to move to the school. The speed of the ship in still water is the same as Jacob's speed and is greater than the speed of the current of river. Once they get to the school, they turn back home. 

Who will get to the home earlier, Jacob, the ship, or at the same time? 

The area of hexagon

 

A square is constructed on each side of a right triangle, as shown in the picture. Express the area of the hexagon DEFGHI in terms of x and y.

Find the digits

 Find the digits X and Y such that the number 2025XY is divisible by 36.