SOLUTION: 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 real

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
--------------------
total time: 1.000 hrs
RELATED QUESTIONS
Jenny ran in a 10 kilometer race. She ran at a rate of 9.5 kilometer per hour for the... (answered by rfer)

In a large marathon, runners start the race in stages. Leanna started in group E and ran (answered by solver91311)

Erica is running a race that is 26.2 miles. She is running at a speed of 8 miles per... (answered by josgarithmetic,MathTherapy)

Julieta ran a marathon of 26 miles in 3.5 hours. During part of the race she ran at 6... (answered by Paul)

A marathoner can run 3/4 of the race in 4/5 hour. At that rate how much of the course can (answered by ewatrrr)

Kerry is training for a bike race that will take place next month. On saturday she rode... (answered by josgarithmetic)

Annie ran a race at a speed of 15m/s in the Time of 8 seconds. Calculate the distance she (answered by Cromlix)

Geri ran in a marathon race. It took her 3 hours and 28 minute to run 26 miles. How many (answered by algebrahouse.com)

In a large marathon, runners start the race in stages. Leanna started in group E and ran... (answered by Alan3354)