CPhill

Thanks, EP

Here's an algebraic solution  :

Let the number of problems Ben solved per day = P

Let the number days that Ben takes = D

So  Anne solved   6( D + 4)  problems  = 6D + 24  problems       (1)

And Ben solved PD   problems          (2)

And Claire solved ( P + 3) ( D - 2)  problems           (3)

So  using (2) and (3)

  PD   = (P + 3) (D - 2)

  PD =  PD + 3D - 2P - 6

  3D =  2P + 6     

  P =  [ 3D - 6 ] / 2          (4)

And subbing (4) into   (2)   and equating to (1) .....we have that

[ 3D - 6 ]   ( D) / 2   =  6D + 24

[ 3D - 6 ] * D  =    12D + 48

3D^2 - 6D =  12D + 48

3D^2 - 18D - 48 = 0

D^2 - 6D - 16  =    0       factor

(D - 8) ( D + 2)  = 0

Since D is positive.....then D = 8

So....the number of problems is 6(8) + 24   =   72

Good job, TwentyFour.....Welcome aboard  !!!!

Grapes of Wrath - Steinbeck......

Only the World's "buoy" problem......others  remain.....

I'd go with EP's.....I think the buoy is floating on the water's surface......and the depth of the water = 8ft

So....the buoy would rise to a height of 13 ft  above the ocean bottom  and fall to a point 3 ft from the ocean's bottom

This makes more sense than mine.....

Try this, Jenny.....but I don't know....EP's interpretation may actually be correct.....!!!!

For the second one, the first sentence is a little confusing.....I'm assuming that  the amplitude is 5 meters...and the midline is 8 metrers below the water's surface....thus the highest point of the buoy is  3 meters below the surface of the water and the low point is  13 meters below the water's surface

Here's the graph : https://www.desmos.com/calculator/6umbpfydcn

Thanks, EP

Note Jenny :  If you have to use the sine function, here's a possibility :

https://web2.0calc.com/api/ssl-img-proxy?src=%2Fimg%2Fupload%2Fc3c1e3de963ed0ca9b1000f1%2Fgraph.png

Reflected about x axis

Shift up 3 units