it took matt twice the time to drive from home to work as it took him to drive back home from work by the same route. if matt averaged 30 miles per hour(mph) on his drive to work, his average speed for the entire round trip was?

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- anonymous

ok so if it was 2 times as fast what would his drive backs mph be?

- EXOEXOEXO

60?

- anonymous

yea

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## More answers

- anonymous

so since you have both of them how do you find the average

- EXOEXOEXO

(30+60)/2?

- anonymous

yea so 45 would be it :)

- EXOEXOEXO

but its not an answer choice

- anonymous

what are the choices???

- anonymous

lol its not twice as fast its twice as slow

- EXOEXOEXO

30
25
40
15

- anonymous

so (15+30)/2

- anonymous

wait a minute

- anonymous

@dan815 am i right in saying (15+30)/2 sorry im tired

- anonymous

lol wait i think im just being dumb

- anonymous

no wait im not it would be 22.5 mph are you sure thats the whole question

- EXOEXOEXO

I think it is a
30+2(15)/2

- anonymous

no then that would just be 30

- EXOEXOEXO

30 mph is the average on Matt's drive to work while 15 mph is the average of Matt's drive to home from work

- anonymous

because he took twice as long using the same rounte meaning he was twice as slow (15 mph) and the other was 30 so the avarage of that is 22.5mph

- anonymous

yea

- anonymous

so basicly in the context of the problem x= matts time from work
so (x+(x/2))/2= avg

- anonymous

and x=30 so

- anonymous

yea

- anonymous

cool @EXOEXOEXO ???

- anonymous

although its not a choice it is the right answer for what you gave me

- EXOEXOEXO

lol

- anonymous

haha yea unless you made a typing error??

- EXOEXOEXO

I don't think I made one

- whpalmer4

How long does it take him to drive to work? How long does it take him to drive home? Add them together to get the round trip time. Average speed for the round trip is round trip distance divided by round trip time.

- anonymous

yea but thats not a choice :(

- whpalmer4

That's all the information you need to calculate the answer...
Let the distance to work be \(x\). Time to drive to work is \(x/30\). Time to drive home is \((1/2)*(x/30)\)
Total distance driven is \(2x\)
Average speed for trip is total distance driven divided by total time.

- anonymous

yea i know that and you would get 22.5 but thats not an answer choice for him

- whpalmer4

No, 22.5 is not the result of that calculation, correctly done.

- whpalmer4

Time to drive to work is \[\frac{x}{30}\]
Time to drive home is\[\frac{1}{2}*\frac{x}{30} = \frac{x}{60}\]
Total time driving is \[\frac{x}{30}+\frac{x}{60} = \frac{3x}{60} = \frac{x}{20}\]
average speed is \[\frac{2x}{\frac{x}{20}}=2x*\frac{20}{x} = \]

- whpalmer4

Or, pick a distance, any distance, and work out the problem.
Let's say it is 60 miles to work, to make the arithmetic easy.
60 miles at 30 miles per hour = 2 hours to drive to work
Driving home takes 1/2 the time, so that's 1 hour to drive home.
Total distance driven is 60+60 = 120 miles.
Total time driving is 2+1 hours = 3 hours
Average speed =

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