SOLUTION: If someone runs the 1st half of a race at 5mph and the 2nd half at 10mph then what's the average speed?

Question 541453: If someone runs the 1st half of a race at 5mph and the 2nd half at 10mph then what's the average speed?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If someone runs the 1st half of a race at 5mph and the 2nd half at 10mph then what's the average speed?
:
let d = the halfway distance of the race
let a = average speed for the whole race
:
Write a time equation, time = dist/speed
:
time at 5mph + time at 10mph = total time
+ =
multiply by 10a, results
2ad + ad = 10(2d)
3ad = 20d
divide both sides by d
3a = 20
a = 20/3
a = 6 mph
RELATED QUESTIONS
Alice is in a 20-km race. She always runs the first half at an average speed of 2 km/h... (answered by ewatrrr)

Your brother competed in a long bicycle race. For the 1st half of the race he averaged... (answered by stanbon)

Q4. A train runs miles at a speed of 30mph, another 50 miles at a speed of 40mph, then... (answered by richwmiller)

Dana has 3 hours to spend training for an upcoming race. She completes her training by... (answered by josgarithmetic,greenestamps)

Arun completes a journey in 11hrs . He travelled the 1st half of the journey at the rate... (answered by JulietG)

Alice is in a 20-km running race. She always runs the first half at an average speed of 2 (answered by ikleyn)

John runs in a race against Matthew. Matthew runs twice as fast as John for the first two (answered by stanbon)

Cindy runs 8 meters/second for half of a 400 meter race. She gets a leg cramp halfway... (answered by stanbon)

The fable about the tortoise an the hare? what? lol (math)? hello this is a math... (answered by rothauserc,robertb)