21. A courier company has motorbikes which can travel 300 km starting with a full tank. Two couriers, Anna and Brian, set off from the depot together to deliver a letter to Connor's house. The only refuelling is when they stop for Anna to transfer some fuel from her tank to Brian's tank. She then returns to the depot while Brian keeps going, delivers the letter and returns to the depot. What is the greatest distance that Connor's house could be from the depot? (A) 180km (B) 200 km (C) 225 km (D) 250 km (E) 300 km

Let A represent the distance Anna goes before transferring fuel. Let C represent the distance to Connor's house. All distances are in km. Here, we will measure fuel quantity in terms of the distance it enables.

The total distance that can be driven by the two motorbikes is ...

2A +2C = 600

Anna can transfer to Brian an amount of fuel that is 300-2A, since she needs to get back to the depot from the stopping point. When they stop, the amount of fuel in Brian's tank is 300-A. After that transfer, the most fuel Brian can have is a full tank (300). Then ...

(300 -A) +(300 -2A) = 300 . . . . fuel in Brian's tank after the transfer

This second equation simplifies to ...

600 -3A = 300

300 = 3A . . . . . . add 3A-300

100 = A . . . . . . . . divide by 3

Using this in the first equation, we get ...

2·100 +2C = 600

2C = 400 . . . . . . . . subtract 200

C = 200 . . . . . . . . . .divide by 2

The distance from the depot to Connor's house can be at most 200 km.