SOLUTION: mr smith traveled for 7 hours and covered 500 kilometers on the trip. During the first part of the trip he averaged 80 kilometers per hour during the second part he averaged 60 ki

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Question 25269: mr smith traveled for 7 hours and covered 500 kilometers on the trip. During the first part of the trip he averaged 80 kilometers per hour during the second part he averaged 60 kilometers per hour, how many hours did he spend on each part of the trip.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
You know that the total distance covered was 500km
At one part the speed was 80kmph
At secodn part the speed was 60kmph
And the total time that took in both add up to 7 hours.
Lets say we want to evaluate the time for 80kmph speed.
Since we can't exceed 7 hours we cant use the "+" sign. and the unknow time is x.
FOr 80kmph the espression looks like this. 80(7-x). 7 being the most hours and x beign the time taken by 80kmph speed.
And sice we don't know the time for 60kmph speed as well we add 60x
totat distance by both = 500
60x+80(7-x)=500
60x+560-80x=500 --> simplfy
-20x=-60
x=3

Do the same for the next
60(7-x)+80x=500
420-60x+80x=500
20x=80x
x=4

60kmph = 4hours, 80kmph = 3hours
Check: 4+3=7hours total.
Hence for 80kmph time taken was 3hours and for 60kmph time taken was 4 hours.
Paul.