Rain Fall#545
Rainfall is measured in millimeters. The rain is collected in a vertical transparent tube with millimeter markings, and once the rain has stopped, one can check the height of the water in the tube.
In this problem, the tube unfortunately has a leak at height millimeters (mm). If the water level rises above the leak, water drains from the tube at a rate of millimeters per hour (mm/h).
We want to determine how much rain fell during a particular rainfall. Assume the tube is high enough so it never overflows. Also, assume rain falls at an (unknown) constant rate, and no water evaporates from the tube. The size of the leak itself is negligible.
One line with five positive numbers: L\ K\ T_1\ T_2\ H, where
is the height of the leak (mm), is the leakage rate (mm/h), T_1 is the duration of rainfall (h), T_2 is the time between the end of rainfall and the observation of the water level (h), and is the water level in the tube when observed (mm).
Each number is at least and at most , given with two decimal places.
Output two real numbers F_1\ F_2, where F_1 is the minimum amount of rain in millimeters consistent with the observation, and F_2 is the maximum amount of rain in millimeters consistent with the observation. Output the answer with absolute error 10^{-9}.
Example 1