SOLUTION: The great runner could travel 10 miles at 5 mph and then run 6 miles at 2 mph. What should be her speed for the next 8 miles so that her overall average speed would be 4 mph. Thank

Question 962956: The great runner could travel 10 miles at 5 mph and then run 6 miles at 2 mph. What should be her speed for the next 8 miles so that her overall average speed would be 4 mph. Thank you in advance!
Found 2 solutions by rothauserc, lwsshak3:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
total distance is 10 +6 +8 = 24 miles and the average speed is 4mph for a total time of 24/4 = 6 hours ( we are using rate * time = distance, which implies that distance / rate = time)
we are given the following distances and rates
10/5 + 6/3 + 8/x where x is the rate while running 8 miles and we know
10/5 + 6/3 +8/x = 6
2 +3 + 8/x = 6
8/x = 1
x = 8 mph
she runs the next 8 miles at 8 mph

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The great runner could travel 10 miles at 5 mph and then run 6 miles at 2 mph. What should be her speed for the next 8 miles so that her overall average speed would be 4 mph.
***
let x=travel time for next 8 miles
average speed=total distance/total travel time
total distance=10+6+8=24
total travel time=10/5+6/2+x=5+x
24/(5+x)=4
20+4x=24
4x=4
x=1 hr
her speed for the next 8 miles=8/1=8 mph
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