We've seen the problems where the minimum amount of pipe is asked for, but here's one a wee bit trickier if anyone would like a go. Nice problem.
"Two houses are located along a straight road, 300 yards apart. A well is to be dug 400 yards from and perpendicular to the main road at a point between the houses, 200 yards from one of the houses. They plan to buy some 1 inch pipe to lay from the well to a junction box and use 400 yards of 3/4 inch pipe they already have to go from the junction to each house.
Where should the junction be located to minimize the amount of 1 inch pipe they need to buy?."
Perhaps someone has a cool approach. I will post my method later.