The 5th little iggy ran all the way at two different rates F

The 5th little [iggy ran all the way at two different rates. First he ran at 8mph for the first third of the trip but soon got tired and slowed down to 5mph for the rest of the two mile trip. Find how many minutes it took the little piggy to get home.

Solution

It states the total distance as 2 mi with 1/3 of that distance ran at 8 mph,
and 2/3 at 5 mph
:
Distance at 8 mph, 1/3(2) = 2/3 mile
Distance at 5 mph, 2/3(2) = 4/3 mile
:
They want the time in minutes, convert given speed to mile per min
8 mph = 8/60 = 2/15 mi per min
5 mph = 5/60 = 1/12 mi per min
:
Time = dist/speed:
:
Total Time = time at 8 mph + time at 5 mph
T =[(2/3)/(2/15)] + [(4/3)/(1/12)]
T = (2/3 * 15/2) + (4/3 * 12/1); invert and multiply
T = (15/3) + (4*4)
T = 5 + 16
T = 21 min total time