If the points P and Q are on the line AB, and AP: Pb = 2:3, AQ: QB = 3:4, and PQ = 4, find the length of ab Map to process (no map is OK) a variety of solutions to complete~

If the points P and Q are on the line AB, and AP: Pb = 2:3, AQ: QB = 3:4, and PQ = 4, find the length of ab Map to process (no map is OK) a variety of solutions to complete~

There are four situations in this question
1、 Points P and Q are on the extension line of segment ba,
Because AP: Pb = 2:3, AQ: QB = 3:4,
So AP = 2Ab, AQ = 3AB,
So AQ -- AP = AB,
Because AQ -- AP = PQ = 4,
So AB = 4
2、 Point P is on line AB, and point q is on the extension of line ba,
Because AP: Pb = = 2:3, AQ: QB = 3:4,
So AP = 2Ab / 5, AQ = 3AB,
So AP + AQ = 17ab / 5,
Because AP + AQ = PQ = 4,
So 17ab / 5 = 4,
So AB = 20 / 17
3、 Point P is on the extension of segment Ba, and point q is on segment ab,
Because AP: Pb = 2:3, AQ: QB = 3:4,
So AP = 2Ab, AQ = 3AB / 7,
Because AP + AQ = PQ = 4,
So 17ab / 7 = 4,
So AB = 28 / 17
4、 Points P and Q are all on line ab,
Because AP: Pb = 2:3, AQ: QB = 3:4,
So AP = 2Ab / 5, AQ = 3AB / 7,
Because AQ -- AP = PQ = 4
So AB / 35 = 4,
So AB = 140