Let the young man ride with the speed 25 km/hr for x hours and with the speed 40 km/hr for y hours respectively.
Money spent at speed 25 km/hr = 50x
And Money spent at speed 40 km/hr = 200y
Maximum distance :
Z = 25x + 40y ….(1)
subject to the constraints
x + y ≤ 1 ….(2)
50x + 200y ≤ 100 ….(3)
x , y ≥ 0 ….(4)
Graph the inequalities (2) to (4). The feasible region (shaded) is shown as below:
Corner Point

Z = 25x + 40y

A (0, 1/2)

20

B (2/3, 1/3)

30Maximum

C(1, 0)

25

Thus, the maximum distance he can travel is30 km.