Assuming that the pipes are to be straight from M to A and B (that is, the pipe does not go to some other point P and then divide), then let's add a couple more points to the diagram:
P: the point on the river bank closest to A
Q: the point on the river bank closest to B
Then PM+MQ = √(20^2-5^2) = √395
Then if M is at distance x from P, it is √395-x from Q.
The amount of piping is AM+BM where
AM^2 = x^2+15^2
BM^2 = (√395-x)^2 + 10^2
So, we have
L = √(x^2+225) + √(x^2-2x√395+495)
L is a minimum when x = 3√(79/5) = 11.92
Not sure what analytical tools you have at your disposal to solve this kind of problem.
Two towns A and B are to get their water supply from the same pumping station to be located on the bank of a straight river that is 15 km from town A and 10 km from town B. If the points on the river nearest to A and B are 20 km apart and A and B are on the same side of the river, where should the pumping station be located so that the least amount of piping is required.
Let M be location and L be amount of piping
L= AM + BM
Found AM^2 and BM^2
Stuck after that
2 answers
Thanks so much. May I know what are the in-between steps for the following two lines please?
L = √(x^2+225) + √(x^2-2x√395+495)
L is a minimum when x = 3√(79/5) = 11.92
L = √(x^2+225) + √(x^2-2x√395+495)
L is a minimum when x = 3√(79/5) = 11.92
1 answer