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Problem of the Week
Problem E
Coffee Run

On Saturday morning at \(8\) a.m., Ayla and Hamza left their house. Ayla walked west towards the beach, and Hamza rode his e-scooter northeast to his favourite coffee shop, then headed to catch up with Ayla. Ayla walked at a constant speed of \(4\) km/h and Hamza rode his e-scooter at a constant speed of \(20\) km/h. If Hamza caught up with Ayla exactly \(45\) minutes after they left their house, what is the maximum possible distance between their house and the coffee shop?

Two arrows point away from a house. One arrow points
horizontally to the left of the house and ends at the beach. The other
arrow points diagonally up and to the right from the house, making a 45
degree angle with the horizontal, and ends at the coffee shop.