Hello, rossco21!

We will use: .

Calum was floating down a river on a raft, when a half-mile downstream,

his brother Duncan set off in a canoe. .Duncan paddled downstream as

quickly as he could, then turned round and paddled back again, still at

his best pace. He arrived back at his starting point just as Calum floated by.

Assuming Duncan's best pace in still water is 10 times that of the river current,

how far did he paddle? Code:

C ½
* - - - - *
D x P
+ - - - - * → → → → → → → → *
* ← ← ← ← ← ← ← ← *
x

Let be the speed of the river's current.

Calum starts at and drifts a half-mile to

. . At mph, this takes him: . hours.

Duncan's speed is mph.

Paddling *with* the current, his speed is: mph.

Paddling *against* the current, his speed is: mph.

Duncan paddles miles downstream from to at mph.

. . This takes him: . hours.

Duncan paddles miles upstream back to at mph.

. . This takes him: . hours.

Duncan's total time is: . hours.

Since Calum and Duncan meet at point , their times are equal.

Our equation is: .

Multiply by miles.

Therefore, Duncan paddled a total of: . miles.