Let "m" be the maximum load which my  track can carry, in pounds.

Let "h" be the maximum load which every her track can carry, in pounds.



The problem says "My truck can carry a load of at least 400 pounds more than each of her trucks".

It means that this inequality is true

    m >= h + 400.    (1)



Next, the problem says "but no more than 7/15 of the total load her four trucks combined can carry".

It means this inequality is true

    m <= .    (2)



For better visibility, let's rewrite inequalities (1) and (2) as one compound inequality

    h + 400 <= m <=     (3)



From this inequality (3), we conclude that THIS inequality is true

    h + 400 <= ,

or, equivalently,

    h + 400 <= .    (4)



We can easy solve it and evaluate "h" from the bottom.  For it, collect the terms with "h" on the right side,
keeping the constant on the left side

    400 <=  - h,

    400 <= ,

     <= h,

     <= h,

    461 <= h,

    h >= 461.


Thus,  "her" truck can carry 461 pounds.

Hence,  "my" truck can carry 400 pounds more, i.e.  461 + 400 = 861 pounds.


ANSWER.  My car can carry 861 pounds, for sure.