SOLUTION: 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?

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Question 133444: 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?
Found 2 solutions by josmiceli, jojo14344:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Distance for whole trip = d
r= average rate for 2nd half
t%5B1%5D= time for 1st half
t%5B2%5D= time for 2nd half
t = time for whole trip
t+=+t%5B1%5D+%2B+t%5B2%5D
t%5B1%5D+=+%28d%2F2%29%2F80
t%5B2%5D+=+%28d%2F2%29%2Fr
t+=+d%2F96
%28d%2F2%29%2F80+%2B+%28d%2F2%29%2Fr+=+d+%2F+96
1%2F160+%2B+1%2F%282r%29+=+1%2F96
multiply both sides by 16r
r%2F10+%2B+8+=+r%2F6
6r+%2B+480+=+10r
4r+=+480
r+=+120km/hr
The train must travel 120 km/hr for the 2nd half
to average 96 km for the whole trip

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
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