Question

a part of the journey is covered in 1 hour 40 minutes at 75 kilometre per hour and the remaining part of it is covered in 2 hours 50 minutes at 60 kilometre per hour find
1) the total length of the journey
2) the average speed during the whole journey

Answer 1

Speed 1 = 75 km/hr
Time   1  = 1 hrs 40 minutes
               = 100/60
               = 5/3 hrs
Distance 1  = Speed * Time
               = 75 * 5/3
               = 25*5
               = 125 km

Speed 2 = 60 km/hr
Time 2    = 2hrs 50 minutes
               = 170/60
               = 17/6
Distance 2 = Speed * Time
                  = 60 * 17/6
                  = 10*17
                  = 170 km

Total distance = 125+170
                       = 295 km

Average speed = Total distance/ Total time
                         = 295/ 10+17/6
                         = 296*6 / 27
                         = 65.7 km/hr

Answer 2

in the first case:
1 hour 40 min=100 min
in hour=100/60=5/3
Distance covered=5/3×75=125 km
in second case,
2 hour 50 min=170 min
in hour=170 /100=17/10
distance covered =17/10×60=102 km.
so,total distance=(125+102) km=227 km.
Average speed=75+60/2
=67.5 km/hour