SOLUTION: On a 100km track a train travells the first 30km at a uniform speed of 30km/h . How fast must the train travel the next 70 km so as to average 40km/h for the entire trip?

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Question 1084090: On a 100km track a train travells the first 30km at a uniform speed of 30km/h . How fast must the train travel the next 70 km so as to average 40km/h for the entire trip?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate x Time = Distance,
For the first 30 km,
30%2At=30
t=1hr
So then to get the average velocity,
Using the distance formula,
1.30%2BV%5B2%5D%2At%5B2%5D=100
and using the average velocity,
2.%2830%2A1%2BV%5B2%5D%2At%5B2%5D%29%2F%281%2Bt%5B2%5D%29=40
So then,
30%2BV%5B2%5D%2At%5B2%5D=40%281%2Bt%5B2%5D%29
Substituting into 1,
40%281%2Bt%5B2%5D%29=100
1%2Bt%5B2%5D=5%2F2
t%5B2%5D=3%2F2hr
So then from 1,
30%2BV%5B2%5D%283%2F2%29=100
V%5B2%5D%283%2F2%29=70
V%5B2%5D=140%2F3km%2Fhr