SOLUTION: A train averaged 120 km/h for the first two thirds of a trip and 100 km/h for the whole trip. Find its average speed for the last third of the trip.

Question 366838: A train averaged 120 km/h for the first two thirds of a trip and 100 km/h for the whole trip. Find its average speed for the last third of the trip.
Found 2 solutions by amoresroy, robertb:
Answer by amoresroy(361) (Show Source): You can put this solution on YOUR website!
A train averaged 120 km/h for the first two thirds of a trip and 100 km/h for the whole trip. Find its average speed for the last third of the trip.
Let x = average speed of train for the last third of the trip
Assume total distance = 360 km
first 2/3 = 240 km
travel time of 1st 2/3 = 240/120 = 2 hrs
If average speed of whole trip is 100 km/h, then total travel time is
360/100 = 3.6 hours
If travel time of 1st 2/3 = 2 hrs, the travel time for last third is 1.6 hr
x = distance of last third / travel time of last third
= 120/1.6
= 75 km/h

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let T = total amount of time of the trip.
Then during the first 2T/3 hours he averaged 120km/hr, and traveled (2T/3 hrs)*(120 km/hr) = 80T km.
For the whole trip, he traveled (T hrs)*(100 km/hr) = 100T km. Therefore in the last third of the trip he traveled 100T - 80T = 20T km. The total time during the last third of the trip is T/3 hours. Hence his average speed for the last third of the trip is (20T km)/(T/3 hrs) = 60 km/hr.
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