How fast can Ron cycle?

[Ergot]

In one hour Dan drives 25 miles farther in his car than Ron can cycle on his bike. If it takes Ron one and a half hours longer to cycle 75 miles than it takes Dan in his car, how fast can Ron cycle?

[Sidoh]

Not sure if this is right.  I'm pretty sick and it's late.

R = D - 25
D = 1.5R
25 = 1.5R - R
25 = R(1.5 -1)
R = 25/.5
R = 50

[Ergot]

Doesn't 50 mph on a bike seem a little umm... far fetched?

[Sidoh]

Doesn't 50 mph on a bike seem a little umm... far fetched?

On average, yeah, but it's definitely possible.  I'm pretty sure I've done it before (downhill, but still).

I see my problem, though... hold on.  Working on a intelligible answer.

[Ergot]

Well I started with rt=D
So r_D*t = (r_R*t) + 25
t = 1 so I get r_D = r_R + 25

75 = r_R(t_D + 3/2)

r_D*t_D = 75
Subsititute this up there...

75 = r_R(75/r_D + 3/2)
Then we plug in r_D that we found in the beginning...
75 = r_R(75/(r_R + 25) + 3/2)
Solving... 0 = 3r_R² + 225r_R - 75

I'm not doing something right... so I tried r=t/d but then that just got me something stupid too x_x

[Nate]

False or 16 2/3 MPH

[Ergot]

False or 16 2/3 MPH

How'd you get it?

[Nate]

t = time, D = Dan's rate, R = Ron's rate
EQ 1.  tD-tR=25 when t =1
EQ 2.  tD = (t+1.5)R
sub  EQ 2 in EQ 1
1.5R = 25
R = 50/3

[Ergot]

According to my calculations... (they might be wrong...)
It'll take Ron 4.5 hours for 75 miles.
It'll take Dan 1.8 hours for 75 miles.
4.5 - 1.8 != 1.5 ? I'm not saying you're wrong... but the difference in their time doesn't work out for me... can you show me Dan's rate/time too ?

[Nate]

I get 37.5 MPH for Dan.

[Ergot]

I get 37.5 MPH for Dan.

Then 4.5 hours for Ron... 2 hours for Dan. That's still not a 1.5 hour difference :( ?

[Joe]

Does this have anything to do with iago and Quik?

[iago]

Doesn't 50 mph on a bike seem a little umm... far fetched?

On average, yeah, but it's definitely possible.  I'm pretty sure I've done it before (downhill, but still).

I see my problem, though... hold on.  Working on a intelligible answer.

Doubt it.  My absolute highest speed (downhill, wind behind me, pedalling as hard as I could) was 58km/h, or 36mph. 

[Sidoh]

Doubt it.  My absolute highest speed (downhill, wind behind me, pedalling as hard as I could) was 58km/h, or 36mph. 

Yeah, but you have a Canadian bike.  Canadian bikes don't have nuclear fuel cells.  Duh.

[BigAznDaddy]

Well I started with rt=D
So r_D*t = (r_R*t) + 25
t = 1 so I get r_D = r_R + 25

75 = r_R(t_D + 3/2)

r_D*t_D = 75
Subsititute this up there...

75 = r_R(75/r_D + 3/2)
Then we plug in r_D that we found in the beginning...
75 = r_R(75/(r_R + 25) + 3/2)
Solving... 0 = 3r_R² + 225r_R - 75

I'm not doing something right... so I tried r=t/d but then that just got me something stupid too x_x

what is all this gibberish