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?

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) (Show Source): You can put this solution on YOUR website!
Distance for whole trip =
= average rate for 2nd half
= time for 1st half
= time for 2nd half
= time for whole trip

multiply both sides by

km/hr
The train must travel 120 km/hr for the 2nd half
to average 96 km for the whole trip

Answer by jojo14344(1513) (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
RELATED QUESTIONS
A train averaged 80 km/h for the first half of its trip. How fast must it travel for the... (answered by solver91311)
In the first half (distance) of a trip, a truck travels at a speed of 40 km/hr. How fast... (answered by ankor@dixie-net.com)
Peggy drives to town at a rate of 40 km/h. How fast must she drive in order to average 80 (answered by ikleyn,Alan3354)
Peggy drives to town at a rate of 40 km/h. How fast must she drive BACK in order to... (answered by Alan3354,ikleyn)
On a 100km track a train travells the first 30km at a uniform speed of 30km/h . How fast... (answered by Fombitz)
A train averaged 120 km/h for the first two thirds of a trip and 100 km/h for the whole... (answered by amoresroy,robertb)
A passenger train making a 240 km trip traveled the first 120 km at 75 km/h. At what... (answered by ewatrrr)
A car averaged 30 MPH for the first mile of a 2 mile trip. How fast would it have to... (answered by ankor@dixie-net.com)
Your average speed on the first half of a car trip is 70.0 km/h. How fast do you have to... (answered by stanbon,Edwin McCravy)