Thread: calculus word problems

I am trying to help a friend with these in preparation for her final. This is a review study guide given to her.

Person X starts walking from point P at a rate of 8.6 ft/sec.
Sixty five seconds later Person Y starts jogging due south from point P at 7.4 ft/sec
At what rate is the distance between the two changing 13 minuets after Person Y begins jogging from point P?

I'm not sure what type of problem this would be or how to set it up? The 13 min seems like a red herring because they are both moving with constant speed. They are not accelerating or it would be in feet per second squared.

It's confusing all the way around... person X is walking faster then person Y is jogging and it seems more like a physics problem to me?


The second question:

An electronics store can sell 60 cellular phones per week at a price of $115. The manager estimates that for each $5 reduction in price she can sell 30 more phones per week. The phones cost the store $35 each. At what price should the store manager set the price so that she maximizes profit?


I dont know about that one either... I never did many calculus word problems.

I think this may involve an integral?

Originally Posted by battleman13

I am trying to help a friend with these in preparation for her final. This is a review study guide given to her.

Person X starts walking from point P at a rate of 8.6 ft/sec.
Sixty five seconds later Person Y starts jogging due south from point P at 7.4 ft/sec
At what rate is the distance between the two changing 13 minuets after Person Y begins jogging from point P?

I'm not sure what type of problem this would be or how to set it up? The 13 min seems like a red herring because they are both moving with constant speed. They are not accelerating or it would be in feet per second squared.
if the direction of motion of person X is constant with time then certainly according to the problem the rate of change of distance between the two persons is constant and there is no sanctity of the '13 min'... it could be very well any other time instant. Probably one of two(or may be both) of the persons have some acceleration. EXAMPLE. person X may be going in circle with constant speed or can have the case of linear acceleration. Note that the direction of walk of person X and person Y may not be same.

It's confusing all the way around... person X is walking faster then person Y is jogging and it seems more like a physics problem to me?


The second question:

An electronics store can sell 60 cellular phones per week at a price of $115. The manager estimates that for each $5 reduction in price she can sell 30 more phones per week. The phones cost the store $35 each. At what price should the store manager set the price so that she maximizes profit?


I dont know about that one either... I never did many calculus word problems.

I think this may involve an integral?

did that help??

Actually to clarify Person X is walking west from point P, Person Y jogging south from Point P.

The way I read this problem:

Person X is walking due west with their position only changing in the negative X direction.
Person Y is jogging due south with their position changing only in the negative Y direction.

It doesn't indicate that either have any acceleration, the problem doesn't state that and the speeds are given in feet per second not feet per second squared.

Which is why I figured the 13 minuets had nothing to do with anything in this problem... It would make no difference if person X started walking 2 years before
person Y did. If they both move at those given speeds then the rate change of distance between them would be the same ?

Originally Posted by battleman13

Actually to clarify Person X is walking west from point P, Person Y jogging south from Point P.

The way I read this problem:

Person X is walking due west with their position only changing in the negative X direction.
Person Y is jogging due south with their position changing only in the negative Y direction.

It doesn't indicate that either have any acceleration, the problem doesn't state that and the speeds are given in feet per second not feet per second squared.

Which is why I figured the 13 minuets had nothing to do with anything in this problem... It would make no difference if person X started walking 2 years before
person Y did. If they both move at those given speeds then the rate change of distance between them would be the same ?

No, 13 min is necessary.i thought that in the problem both are walking in the same direction and so i said that 13 min is useless. but since one is walking west and one is walking south their 'SEPARATION VECTOR' is changing with time. the relative velocity vector from X to Y(or Y to X) is definitely constant. BUT the the rate of change of distance between the two is the COMPONENT of the relative velocity vector ALONG the separation vector. this certainly depends on the time instant you want to find the rate of change of distance at.