Question 20748
Okay here goes, 
Before I start the solution please notice that the time is in minutes but the distance is in miles/hr. 


Information given, 
Total Time, t = 30 mins or 1/2 hr or .5 hr 
Total distance, d = 2.5 miles/hr 
Rate of walking Rw = 0.05 miles/min or 3 miles/hr
Rate of jogging Rj = 0.1 miles/min or 6 miles/hr 


To Find, 
Time jogged, Tj = ?
Time walked, Tw = ? 


Let Dj be the distance jogged and Dw be the distance walked 


Dj + Dw = 2.5 ------------ Equ (1) 
Tj + Tw = 0.5 ------------ Equ (2) 


We know that 
D = T x R 
so,
Dw = Tw x Rw 
Dj = Tj x Rj 


Replace the above in Equ (1) 
(Tw x Rw) + (Tj x Rj) = 2.5 -------------- Equ (3) 


From Equ(2) we get, 
Tw = 0.5 - Tj, 
So Equ (3) becomes 
[(0.5 - Tj) x 3] + (6 x Tj) = 2.5 
Solving the above equation for Tj we get, 
Tj = 1/3 hr 

Since, 
Tw + Tj = 1/2 
Tw = 1/2 - 1/3 
Tw = 1/6 

Time spent walking is 1/6 hr or 10 mins
Time spent jogging is 1/3 hr or 20 mins