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# There and Back

##### Stage: 4 Challenge Level:

In this problem, consider the following:
When Brian swims with the flow, his total speed is his speed in the water plus the speed of the moving water. When he swims against the flow, his total speed is the difference between his speed in still water and the speed of the moving water.

This leads to the following solution:

Let the speed of the river be v , distance to the moored boat = d , and the time to complete the downstream journey = t .

 Downstream Upstream Speed of man = 3 v Speed of man = v Distance = d Distance = d Time = t Time = 12 - t

Again, using distance = speed x time, gives the following equations:

(1) d = 3 vt

(2) d = v (12- t )

combining (1) and (2) gives

3 vt = v (12 - t )

which leads us to t = 3 minutes

Using this information tells us that the speed of the river is d/9

and since Brian swims at twice this speed, his speed in the still water is 2d/9.

He swims a distance of 2 d at this speed.

So it will take him 9 minutes.

Correct solutions were sent from Nicholas and Adrian (South Greenhoe Middle School).