A train averaged 80 kmh for the first half of its trip How f

A train averaged 80 km/h for the first half of its trip. How fast must it travel for the second half of the trip in order to average 96 km/h for the whole trip?

Solution

Let\'s designate A = 80 km/hr for the first 1/2 of trip.
Then, designate B = x (unknown) for the other 1/2 of the trip.
So, to get the speed of B (the other half of the travel) to arrived at an average of 96 km/hr:
(A + B)/2 = Average
substituting, A= 80 km/hr; B = x; Average = 96 km/hr
so,
(80km/hr+ x) / 2 = 96 km/hr
80 + x = 2*96
x = 192- 80 = 112 km/hr. This should be the speed on the next half hour to have an average of 96km/hr.
To check: (A + B) / 2 = (80+112)/2 = 96 km/hr (average which is given)
So,
having B = 112 km/hr is correct because the equation will arrived to the given average of 96 km/hr