If you can't solve the retard test, you have no business posting on Veeky Forums

if you're too NEET for this it's 20 miles

>having to cuckold yourself into buying an Ozone Killer, Cancer Radiator, Death Trap On Wheels
Good goy.

>Implying I care about the environment or others
L O L
O
L

>answer is approximately 29.52 miles away

You never made it clear whether or not he lives in his car, or whether the road has curves, shortcuts, corkscrews, loops or anything that might extend the trip, making it longer than what it actually is

It seems the retard here is you.

Avg speed of the round trip is 2*80*25/(80+25) = 800/21 mi/hr

Time = 63/60 hour
RT distance = (800/21)*(63/60) = 40 miles
40/2 = 20
Therefore by the fundamental theorem of calculus, he lives 20 miles away.

Wouldn't it be easier just to go on google maps and measure the distance from his work place to his house?

ITT: everyone does 15 year old OP's homework

How did you get the average speed of the round trip?

25 miles something maybe 26-27

Average speed of trip is just 2*slope

Hahahahahahaha

>80mph to work
The fucking madman

Slope of what? The displacement vs time curve? I don't see where 80*25/(80+25) is coming from.
He got the right answer though. Was it just a fluke? I'm trying to get at the reasoning.

If X is the solution he drove 2x miles in 73 minutes. That means he drove 2x miles in 73/60 hours, which is actually 73 minutes.

If he sped at 80 mph on the way there and went 25 on the way back, then he took 80/25 times longer on the return trip. If Y represents how long it took him to get there at 80 mps, Y + 80Y/25 then represents the total time he spent, which is 73 minutes.

73 minutes = 105Y/25 = 17.38 minutes to get there at 80 mph. Multiply 80 mph by 17.38min/60min and you get 23.17 miles from home.

Jesus fucking Christ.

Except I'm a triple nugget and misread 1 h 3 minutes as 1 hour 13 minutes.

Area of mph/mph

Look the total time T is the time it took to get there and the time it took to get back. That means

T = t1 + t2

You know that the distance traveled is equal to the velocity multiplied by the time. How fast you were going per second * how many seconds.

On the way there,

d = v1 * t1

on the way back

d = v2 * t2

solving for t1 and t2 gives you

t1 = d / v1 and t2 = d/v2

We have T = t1 + t2 and so

T = d / v1 + d / v2

T = d (1 / v1 + 1 / v2 )

= d (v1 + v2) / (v1 * v2)

solving for d,

d = T (v1 * v2) / (v1 + v2)

Yes I understand how to solve the problem. That's exactly how I did it. But (v1*v2)/(v1+v2) didn't pop up until the very end when we solved for the distance. I'm wondering how that user got it in his first step.

Please explain.

>1.05
Are you fucking kidding me

Wait a minute isnt it 20 miles?
This takes 15 minutes at 80mph and 48 minutes at 25 mph
Wtf sci

How i found it.
If it takes you 1 unit of time to go x distance at 80 mph, it will take you 3.2 times as long to go the same distance at 25 mph (80/25). So the total amount of time is 4.2 units of time, 1 there and 3.2 back. So 63 minutes divided by 4.2 is 15 minutes, which is how long it takes to drive x distance at 80 mph. 15 minutes is 1/4th of an hour, 1/4th of 80 mph is 20 miles

1.05 = 1 and 1/20
60/20 = 3 minutes
No im not fucking kidding you

I guess most people don't even get WHY a harmonic mean works the way it does.

[math]\frac{1}{\frac{(x miles) * \frac{1 hour}{80 miles} + (x miles) * \frac{1 hour}{25 miles}}{2 * (x miles)}}=
\frac{1}{\frac{(x miles) * (\frac{1 hour}{80 miles} + \frac{1 hour}{25 miles})}{2 * (x miles)}}=
\frac{1}{\frac{\frac{1 hour}{80 miles} + \frac{1 hour}{25 miles}}{2}}=
\frac{2}{\frac{1 hour}{80 miles} + \frac{1 hour}{25 miles}}=
\frac{800 miles}{21 hours}[/math]

[math]\frac{800 miles}{21 hours} * (1 hour + 3 minutes * \frac{1 hour}{60 minutes})=40 miles[/math]

I should add (had forgotten), that 40 miles is the total length of the round-trip.

So half that, would be the length of x.
[math]20 miles[/math]

How do I format nicely in TeX?

So his trip at 80mph took 15 min and
his trip at 25mph took 48 min.

Illegible answers will not receive any marks.

I just came on this board for the first time to see if intelligent discussion goes on here.

Instead, the very first thread is another /b/-tier bait math question with ambiguous wording.

63/60=5x/400+16x/400
63/60=21/400x
x=63/60*400/21=400/60*63/21=40/6*3=40/2=20

"illegible"

20 miles.

80/(80+25) gives you the ratio of time he was driving 25 mph, multiply that by 1.05 hours to get the amount of time he spent driving at 25 miles per hour. then multiply that time by 25 mph.

Trip back: 80/25 = 3.2t
Trip there: t
63 min/d+3.2d = 15
15/60*80 = 20

meant to say t for all variables

>by the fundamental theorem of calculus
kek

This is the correct answer.

That's what I got.
X = distance Bob-work
H = Time for trip Bob-work
Y= time for trip work - Bob
X/H=80
X/Y = 25
H+Y = 1 and 3/60
(X/80) + (X/25) = 1 and 1/20
5X + 16X = 420
21X = 420
X = 20

Why are you retards doing this kid's homework?

The real answer is that Bob is in jail for going 80 mph to work the absolute madman.

Assuming that his total time was 1 hour 3 minutes then because that is 1.05 hours (3/60=0.05), and total time(in what would be % of hours)=distance/speed,
1.05=(x/80)+(x/25) with the slashes being fraction bars
x/80+x/25
5x/400+16x/400=21x/400
1.05=21x/400
420=21x
20=x

He lives 20 miles away, but he has a lot more problems than that

20 miles