Question 709687: Miranda trained consistently, so that she can finish a race in 1 hour. During the race, she ran at the rate of 8 kph. However, upon reaching the halfway point of the race, she realized she needed to run faster so she can increased her speed to 10 kph. If she reached her goal just in time, how long was the race?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! finish a race in 1 hour.
During the race, she ran at the rate of 8 kph.
However, upon reaching the halfway point of the race, she realized she needed to run faster so she can increased her speed to 10 kph.
If she reached her goal just in time, how long was the race?
:
Let d = distance of the race
:
Write a time equation; time = dist/speed
:
8km time +10km time = 1 hour
 +  = 1
multiply by 40 to clear the denominators, resulting in:
5(.5d) + 4(.5d) = 40
2.5d + 2d = 40
4.5d = 40
d = 40/4.5
d ~ 8.89 km is the distance of the race
:
:
Check this by finding the actual time at each speed
4.445/8 = .5556 hrs
4.445/10 = .4445 hrs
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total time: 1.000 hrs
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