Help!!!!!!! A boy, 3 meters tall, walks away from a lamp fixed at a height of 10 meters from the ground. He walks at a constant rate such that the length of his shadow increases at a rate of 3 m/s. At what rate is the boy walking?

I think we have to use the similar triangles concept since the ratio of the sides remains constant..

Question

Help!!!!!!! A boy, 3 meters tall, walks away from a lamp fixed at a height of 10 meters from the ground. He walks at a constant rate such that the length of his shadow increases at a rate of 3 m/s. At what rate is the boy walking?

I think we have to use the similar triangles concept since the ratio of the sides remains constant..

anonymous · Answer

sounds like a "related rates" question...I gotta step out for a bit..I'll help you on this one if it still isnt answered when I get back :)

anonymous · Answer

okay.. :)

anonymous · Answer

Do you have the answer? I got 10m/s. Is it right?

anonymous · Answer

Well.. The hint says the final answer is a fraction..

anonymous · Answer

I know where I was wrong..wait..

anonymous · Answer

kay (:

anonymous · Answer

Oh.no I got 7!...Anyway. I tell my thought. suppose v is the speed of the man and s is the length of his shodow. Then they have: 3/10=s/(s+vt).  t is time.  
=> s=3/7v*t
ds/dt=3/7*v=3  get v=7 m/s...

anonymous · Answer

I am not an English person. I wish I can use my words more accurate.
By the way. I am studying the linear algeba..

anonymous · Answer

Ohh thats interesting! (: & That's okay that's why I like math because its the same in every language :D & Thanks for your time:)

anonymous · Answer

If you got the right answer. Don't forget to tell me. I want to know where is my mistake. I really expect it.

anonymous · Answer

(3/7)m/s is the correct answer

anonymous · Answer

I mean the whole solution...

anonymous · Answer

Yeah similar triangles is the way to solve this one here. A diagram to reference is found here: http://mathcentral.uregina.ca/QQ/database/QQ.09.07/s/casey1.html We have:$$10/3=\frac{x+w}{w}$$Here x is the distance the boy is from the lamp. w is the length of his shadow. Both w and x are functions of time. We are given dw/dt=3. This represents the changing length of the boy's shadow as he walks away from the lamp. We want dx/dt which is the speed at which the boy is walking away from the lamp. I'll re-write the above as:$$(7/3)w=x$$Now we differentiate both sides with respect to t (using the chain rule):$$(7/3)dw/dt=dx/dt$$Inputting our known dw/dt=3 and solving for dx/dt we get:$$(7/3)3=7$$As far is I can tell this is correct (but your hint says we are supposed to get a fractional answer?!)...

anonymous · Answer

yeah i confused myself. its said the derivative of a fraction is the answer