SOLUTION: In the first half (distance) of a trip, a truck travels at a speed of 40 km/hr. How fast must it go during the second half of the trip to average 50 km/hr for the entire trip?

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Question 944356: In the first half (distance) of a trip, a truck travels at a speed of 40 km/hr. How fast must it go during the second half of the trip to average 50 km/hr for the entire trip?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In the first half (distance) of a trip, a truck travels at a speed of 40 km/hr.
How fast must it go during the second half of the trip to average 50 km/hr for the entire trip?
:
Let s = speed required on the 2nd half to average 50 km/hr
let d = half the distance of the trip
Write time equation; time = dist/speed
:
1st half time + 2nd half time = total time
d%2F40%29 + d%2Fs = %282d%29%2F50
multiply equation by 200s
200s*d%2F40%29 + 200s*d%2Fs = 200s*%282d%29%2F50
cancel the denominators and you have
5ds + 200d = 4s(2d)
5ds + 200d = 8ds
Get rid of d, divide thru by d
5s + 200 = 8s
200 = 8s - 5s
200 = 3s
s = 200/3
s = 66.67 km/h on the 2nd half of the trip
:
:
We can confirm this by choosing a distance (200 km half-way) and substituting for s, find the times
200%2F40%29 + 200%2F66.67 = 400%2F50
5 hrs + 3 hrs = 8 hrs