i Need help in solving this word problem

Question

In an experiment on motivation, Professor Brown trained a
group of rats to run down a narrow passage in a cage to receive food
in a goal box. He then put a harness on each rat and connected it to
an overhead wire attached to a scale. In this way, he could place the
rat different distances from the food and measure the pull (in
grams) of the rat toward the food. He found that the relationship be-
tween motivation (pull) and position was given approximately by
the equation

         P= -1/5(d) + 70     30 ≤d ≤ 70
where pull p is measured in grams and distance d in centimeters.
When the pull registered was 40 grams, how far was the rat from
the goal box?

Answer 1

Nauman,

 

There is something wrong in your formula as stated, besides the semantics of measuring a force (the pull) in units of mass (grams).

 

Any way, if I interpret -1/5(d) as -(1/5)d,  then   -(1/5)d = 40 - 70 = -30  implies d = 150 which is outside your permissible range.

 

If I interpret -1/5(d) as -1/(5d), then -1/(5d)= 40 - 70 = -30 implies d = 1/150 which is also outside your permissible range.

 

Perhaps the problem is the sign on the 40 grams.  Maybe it should be negative?  Then the two interpretations yield the following solutions:

 

If I interpret -1/5(d) as -(1/5)d, then -(1/5)d = -40 - 70 = -110 implies d = 550 which is still outside your permissible range.

 

If I interpret -1/5(d) as -1/(5d), then -1/(5d)= -40 - 70 = -110 implies d = 1/550 which is also outside your permissible range.

 

So that didn't fix your formula.  Anyway, once you get your formula straightened out, and clarify whether d is in the numerator or the denominator by using parentheses or 0.2 for 1/5, then solve it as above. And check to see that the solution fits your constraint on d.

 

Maybe that rat has to get "pumped up" by Hans & Franz like Packers QB Aaron Rodgers did in a commercial so you get better data.