Question 603675
Distance = speed * time

Time = distance/speed

t=d/r
First condition

Time  Part I + time part II = 2.5 hour

30/x+90/y = 2.5

Let 1/x=a & 1/y = b

30a+90b=5/2.......................(1)

Second condition

90/x+30/y = 2 1/6 = 13/6

90a+30b= 13/6......................(2)

add (1) & (2)
120a+120b=5/2+13/6
120a+120b=14/3
divide by 120
a+b= 14/360.............(3)

(1)-(2)

-60a+60b=1/3 
divide by -60
a-b=-1/180...................(4)

(3)+(4)
2a= 14/360-1/180

a=7/360 -1/360
a= 6/360
a=1/60
1/x= 1/60
x= 60 


a+b = 14/360
b= 14/360 -1/60
b=8/360
b=1/y = 8/360
y= 360/8
y=45