Maximum and Minimum Question (Fitzpatrick) (1 Viewer)

[Equilibrium1]

Can someone please help me out with this question? Thanks heaps =)

"Two straight roads intersect at right angles. Two men, A and B, are 100 kilometres 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?"

I really appreciate any kind of help.

Thank you
=)

 

[Equilibrium1]

Bump ^

Please Help!
=)

 

[deswa1]

The way to do this question is:
After 1 hour, A will have travelled 30km and B will have travelled 40km. Extending this, after time T, A will have travelled 30T km and B will have travelled 40T km. Therefore the distance from the intersection will be 100-30T for A and 100-40T for B. To find their distance apart, note that the road intersects at right angles. Therefore Pythagoras's theorem applies. Denoting the intersection by O, the distance between them is the square root of OA^2 + OB^2. Finally, to minimise the distance, differentiate this expression, solve for stationary points and then test whether its a maximum or minimum.

Hopefully that helps If you still can't do it, I might be able to post a complete solution.