John's Responses in WyzAnt Answers

Let x equal the number of hours at the pharmacy and y equal the number of hours babysitting. Then

15x +10y = 90

Now the last part of your question did not show up above but I am assuming that the total hours where specified, let call that T. So the second equation is:

x + y = T

Then these equations can be solved by substitution or any other preferred method of solving simultaneous equations.

The difference between the first and second numbers is 4, between the second and third is 6, between the third and fourth is 8. What do you notice about this? Is it a pattern that continues?

The potential energy of the pinecone before it drops is mgh (given the ground is used as the zero potential energy reference). After if falls the energy is all kinetic energy or (1/2)mv^2 Equating these gives v^2 = 2gh. Note that you can now determine the energy loss due to air friction by the difference in kinetic energy of the two cases. You will need the mass for this calculation.

Just in case you are not taking a calculus level class, the position can be deterimined by the area under the curve of the velocity graph up to the time in question. If the graph drops below the x axis, count this as negative area.

We know from the first part that the distance is equal to the speed multiplied by the time

d = st, or d = (45 mi/hr)t

we also know from the last part this same distance is

d = (60 mi/hr)(43 mi - 10 mi - t), or (60 mi/hr)(33 hr - t).

Now elliminate the d

(45 mi/hr)t = (60 mi/hr)(33 hr - t)

and solve for t.

Note: In professional work it is always a good idea to keep track of the units this way (they operate mathematically the same way as variables). But for this math problem it may be best to drop them. Do what's best for you though.