Pension Proportions and Service Lengths

Two persons are awarded pensions in proportion to the square root of the number of years they have served. One has served 9 years longer than the other and receives a pension greater by $\pounds 50$. If the length of service of the first had exceeded that of the second by $4\frac{1}{2}$ years their pensions would have been in the proportion of $9:8$. How long had they served and what were their respective pensions?

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. III. Variation, Examples III, No. 20