Hello, afan17!

I'm new to this forum . . . Welcome aboard!

I'm actually tutoring a refugee in a volunteer program . . . Good for you!

A resort has a rectangular swimming pool ABCD with AB = 75m, AD = 30m.

P is a point somewhere between D and C.

A boy can swim at 1 m/s and run at 1 2/3 m/s.

He starts at A, swims to point P, and runs from P to C.

He takes 2 seconds to pull himself out of the pool.

a) Let DP = x meters and the total time be T seconds.

Show that: . Code:

A 75 B
* - - - - - - - - - - - - - - *
| * |
| * |
30 | * |
| * |
| * |
* - - - - - - - - * - - - - - *
D x P 75-x C

He will swim the diagonal distance

This is the hypotenuse of right triangle

. . Hence:. .

At 1 m/sec, this takes him: . seconds.

He runs the distance m/sec.

This takes him: . seconds.

He also used 2 seconds to leave the pool.

His total time is: . seconds.

b) Find We have: .

Then: .

c) (i) Find the value of for which is a minimum.

(ii) Find the minimum time. (i) Solve

We have: .

Square both sides: .

. .

(ii) Substitute into the formula in part (a).

d) Find the time taken if the boy runs from A to D and then D to C. He would run: . meters at m/sec

This will take him: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Very funny!

If the boy's only concern is getting from to as fast as possible,

. . he should all the way (and skip the math).

However, if this some sport where __some__ swimming is required,

. . then our solution provides the shortest time.