Question

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?

Answer 1

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

Answer 2

60?

Answer 3

yea

Answer 4

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

Answer 5

(30+60)/2?

Answer 6

yea so 45 would be it :)

Answer 7

but its not an answer choice

Answer 8

what are the choices???

Answer 9

lol its not twice as fast its twice as slow

Answer 10

30
25
40
15

Answer 11

so (15+30)/2

Answer 12

wait a minute

Answer 13

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

Answer 14

lol wait i think im just being dumb

Answer 15

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

Answer 16

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

Answer 17

no then that would just be 30

Answer 18

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

Answer 19

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

Answer 20

yea

Answer 21

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

Answer 22

and x=30 so

Answer 23

yea

Answer 24

cool @EXOEXOEXO ???

Answer 25

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

Answer 26

lol

Answer 27

haha yea unless you made a typing error??

Answer 28

I don't think I made one

Answer 29

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.

Answer 30

yea but thats not a choice :(

Answer 31

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.

Answer 32

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

Answer 33

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

Answer 34

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 \[\frac{2x}{\frac{x}{20}}=2x*\frac{20}{x} = \]

Answer 35

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 =