Let's assume that the initial hourly pay for Lan is 5x, and the initial hourly pay for Laura is 4x.
After receiving an increase of £1.50 in their hourly pay, Lan's new hourly pay becomes 5x + £1.50, and Laura's new hourly pay becomes 4x + £1.50.
According to the given information, the ratio of Lan's hourly pay to Laura's hourly pay after the increase is 11:9. Therefore, we can set up the following equation:
(5x + £1.50) / (4x + £1.50) = 11/9
To solve this equation, we can cross-multiply:
9(5x + £1.50) = 11(4x + £1.50)
45x + 13.50 = 44x + £16.50
Now, we can solve for x:
45x - 44x = £16.50 - £13.50
x = £3.00
Therefore, the initial hourly pay for Lan was 5x = 5 * £3.00 = £15.00, and the initial hourly pay for Laura was 4x = 4 * £3.00 = £12.00.