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# Math Problem for you

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I do cycling on the road.

I did a ride that was 19.5 miles. My average speed for that distance was 19.17mph. At mile 14.5 my average speed was 17.00mph. What was my average speed for the last 5 miles of the ride? If you can tell me and wow how you did the problem, I'd really appreciate it!
thanks =)

Should be easy:

For the whole trip, you needed 1.017 hours, that is, 3661 seconds (rounded to nearest integer).

At the 14.5th mile, with that stated average speed of 17 mph, you already had ran for 0.853 hours, or 3071 seconds (rounded to nearest integer).

That leaves you with 590 seconds or 0.164 hours to complete the remaining 5 miles.

Which in turn results in 5/0.164 = 30.5 mph (again, rounded up)

Quite unlikely this was a real ride, unless your bicycle is motorized or you're Lance Armstrong ;-)

Maes said:

Should be easy:

For the whole trip, you needed 1.017 hours, that is, 3661 seconds (rounded to nearest integer).

At the 14.5th mile, with that stated average speed of 17 mph, you already had ran for 0.853 hours, or 3071 seconds (rounded to nearest integer).

That leaves you with 590 seconds or 0.164 hours to complete the remaining 5 miles.

Which in turn results in 5/0.164 = 30.5 mph (again, rounded up)

Quite unlikely this was a real ride, unless your bicycle is motorized or you're Lance Armstrong ;-)

Hehe.. that's why I posted the problem, because I was going so fast for the last 5 miles I wanted to know what my average speed was. Thanks solving this for me! It was a real ride. The first 4.5 miles was a very gradual incline. The second 4.5 miles was a moderate incline. The last 5 miles was all down hill, a little steeper than the ascent. http://www.mapmyride.com/ride/united-states/ma/amherst/219125288390211317 look for the little elevation checkmark in the upper right corner. Lance would have averaged 29mph, not 19mph :P

Wow. I wouldn't allow any of the bikes I own to develop 30 mph downhill, it would take like 200m or more meters to stop, unless I did the secret "shoe brake" technique and hoped for the best :-p

lol, well i have a decent bike. It was pretty sketchy tho towards the end as I think the blood to my head was becoming restricted from my crouched down posture. I spent most of the time at 30+ and 40+ mph. My top speed was 48.84.

Last time I went that fast I had to use my face brake.

Pft, road bikes. I'll run you over with my mountain bike.

exp(x) said:

Pft, road bikes. I'll run you over with my mountain bike.

yeah, just try to catch me.

Maes said:

"shoe brake"

I remember my real poor friend didn’t have working brakes on his bike so he had to do that.

exp(x) said:

Pft, road bikes. I'll run you over with my mountain bike.

Word. I need to get mine back in working order.

Bikes suck. Motor vehicles FTW.

ololo fatty

Fisk said:

Up a furry orifice, you yiff.

Hey that kinda rhymes.

Hellbent said:

yeah, just try to catch me.

Just try to even ride on my trails at all.

Wow, thats pretty fast for a bicycle.

Well I do mostly mountain biking, so I highly doubt that my bulky mountain bike and knobby pavement slapping tires could do 30mph LOL And my brakes are crap :O

what kind of bike do you have?

Maes said:

Wow. I wouldn't allow any of the bikes I own to develop 30 mph downhill, it would take like 200m or more meters to stop, unless I did the secret "shoe brake" technique and hoped for the best :-p

Nah, that's just fun. Outside my village there is one of those electronic signs that flash if you are going above the speed limit coming into the village (30mph). It is also down hill and I love trying to get it to flash when I'm on my bike - and I quite often manage. On the times that I don't get it to flash, sometimes I'm sure that it doesn't simply because it isn't too good at detecting a small target rather than me not peddling fast enough. :)

r_rr said:

what kind of bike do you have?

I have these

r_rr said:

Wow, thats pretty fast for a bicycle.

Well I do mostly mountain biking, so I highly doubt that my bulky mountain bike and knobby pavement slapping tires could do 30mph LOL And my brakes are crap :O

what kind of bike do you have?

I have a Giant OCR something or other.. it's a \$3,000 bike with some recent upgrades to make it faster, like faster tires, better, lighter pedals and high performance shoes. I'm very lucky to have a brother who owns a bike shop.

I did another ride today: similar route but I took a funky detour; went the wrong way a couple times requiring a couple U turns bringing down my average.

Total distance: 23.5mi
Top speed: 39.59mph
Avg speed: 19.62mph
Avg speed at top of shutesbury hill: 17.23

Generally speaking with rides that end where they start, the higher your top speed the lower your average speed. I'll leave you to puzzle the reason for that! :D Although there is an exception to this rule.

Hellbent said:

yeah, just try to catch me.

Hard to do with a mountain bike. I have a street/mountain bike hybrid, and the top speed I got from it on a very steep hill, was almost 37MPH. On a lesser hill, a racing bike I had, I got to about 44MPH.

When I bike to work (very small window of opportnity up here in New England, with my hours, and travel distance), it's about 18 miles to work, over 16 on the way back, averaging about 17MPH going to work, about 13MPH heading home.
The discrepency in milage is due to a safer way to work being a bit longer. Going home, no way is safest, so I go the shortest route.

cool, where in New England are you?