Two more measuring problems

See the previous two measuring problems

You have two lengths of rope. Each one takes exactly one hour to burn. However, they are not necessarily identical in length or size. In fact, neither of them is uniform. That is, after half an hour of burning, there might not be exactly half of the original length remaining. Therefore, you cannot simply wait for the fire to reach the half-way point and assume that exactly 30 minutes have passed.

Use these two ropes to measure 45 minutes.

And now for the challenge problem! It's an old one that I had written, and now it's yours.

You have three unmarked, asymmetrical containers, and no others. The first holds 6 cups, the second holds 10 cups, and the third holds 15 cups. The 10-cup pitcher is filled with lemonade, but it's too strong. You need to dilute it to half of its current concentration. You have an unlimited source and sink for water, but please don't throw out any of the lemonade! Remember, all the lemonade must be diluted to half-concentration.

Solutions have been posted, or you can just read the comments below.