let the original rate be x miles/hr
distance covered on first leg = (24/60)x = 2x/5 miles
distance covered on his second leg = (6/60)(x-10) = (x-10)/10
remaining distance = 80 - 2x/5 - (x-10)/10
time for remaining distance = (80 - 2x/5 - (x-10)/10 )/1.5x
time had he gone the whole distance at x mph = 80/x
sum of times of 3 legs + 22/60 = time at one speed
24/60 + 6/60 + (80 - 2x/5 - (x-10)/10 )/(1.5x) + 22/60 = 80/x
2/5 + 1/10 + (80 - 2x/5 - (x-10)/10 )/1.5x + 11/30 = 80/x
13/15 + (80 - 2x/5 - (x-10)/10 )/1.5x ) = 80/x
times 15x
13x + 10(80 - 2x/5 - (x-10)/10 ) = 1200
13x + 800 - 4x - x +10 = 1200
8x = 390
x = 390/8 = 48.75 mph
check:
distance of 1st leg = (24/60)(48.75) = 19.5 miles
distance of 2nd leg = (6/60)(38.75) = 3.875
distance left = 80-19.5-3.875 = 56.625 miles
at speed of 50% more or 73.125 mph, time = 56.625/73.125 hrs or 46.46 min.
total time = 24+10+46.46 or 80.46 min
time going at one speed of 48.75 = 1.6410 hr or 98.46 min
difference = 98.46 - 80.46 = 18
ARGGGG, should have been 22
Can't find my arithmetic error, see if you can find it.