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Math Help - [SOLVED] Application of Differentiation

  1. #1
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    Exclamation [SOLVED] Application of Differentiation

    Hey guys

    Two straight roads intersect at right angles. Two men, A and B, are 100 km from the intersection, one on each road. They drive towards the intersection at 30 km/h and 40 km/h respectively. Find the distance of each driver from the intersection as a function of t, the time in hours for which they are driving. Hence, find their distance apart, d(t), at any time. For what value of t is their distance apart least?

    How exactly do I do this question? I don't seem to get it .

    Please help?
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  2. #2
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    So sorry!

    I solved it after staring at the question for 10 minutes (after i posted it ).
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  3. #3
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    How did you solve it?

    Hi there, mind to share your solution? Thanks!
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  4. #4
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    I presume it suddenly occured to you to use the Pythagorean theorem? If t is the time, in hours, after the intial point, then the distance of each to the intersection is 100- 30t and 100- 40t. The straight line distance between them is D= \sqrt{(100- 30t)^2+ (100- 40t)^2}.

    That will be minimized when D^2= (100- 30t)^2+ (100- 40t)^2 is minimized, so you don't have to worry about differentiating the square root.
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  5. #5
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    Thanks so much.

    So, the next step would be to differentiate D wrt t, equate dD/dt = 0 and find t?
    I'm getting weird equations upon calculating t.
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