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# Mike and Ike’s Trike

## Question

Mike and Ike buy a trike and ride in circles around a spike. They each ride at a different time of day. They both pedal at the same rate. They both make perfect circles with the spike at the exact center. Mike rides twice as long (time) as Ike, but they cover the exact same distance. How is this possible?

(Edit - minor change in terms)

Edited by Smith

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Mike is half as far from the spike

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It says they buy "a trike", but is it safe to assume they are riding the SAME trike?

Edited by scuttill
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They are on the beach and mike rides when the tide is in, meaning he has more resistance against him and so takes longer.

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I agree with Simon.

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Mike is twice the distance from the spike as Ike.

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Mike is half as far from the spike

No, that is an interesting idea, but you are not correct. Sorry.

It says they buy "a trike", but is it safe to assume they are riding the SAME trike?

Yes, that is a safe assumption. They ride the same trike and they pedal it at the same rate.

They are on the beach and mike rides when the tide is in, meaning he has more resistance against him and so takes longer.

No, they pedal at the same rate, rotationally speaking. You could argue that they are exerting the same ENERGY due to the presence of the water, but that was not my intention.

I agree with Simon.

I must therefore disagree with your agreement, though it pains me to say so.

Mike is twice the distance from the spike as Ike.

Another interesting concept, I admit. Would you care to expand upon this?

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How do you define distance? I remember my physics teacher talking about displacement- the distance between the start and end point. If Ike completed a whole number of circles (1, 2, 3, etc), the displacement would be 0. If Mike rides in a circle with the same radius, going around for twice as long, he would also end at the start point and the displacement would alsi be 0.

Probably not what you are looking for but might as well try.

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The spike is in the middle of a playground carousel. One of them rides against the spin of the carousel, one of them rides with the spin. To an outside observer on solid ground, one has covered more distance than the other without pedaling any faster..

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It is possible if you define "distance" in terms of angles instead of the usual metric.

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Mike and Ike's trikes are not alike. Mike's wheels could be half the diameter of Ike's.

Or maybe Mike spent the first fourth of his time peddling backwards.

Or maybe Mike is quite light such that his mass and the trike is not enough to get constant traction.

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I find WitchOfDoubt's answer meaningful here.

T(mike)=2 * T(ike)

D-linear(mike) = D(linear)-Ike

=>V-linear(mike)=1/2*V-linear(ike)

Since they pedal at the same rate, the ground/platform under mike is moving with linear velocity of (1/2) as that of ike in the opposite direction.

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Since there was the mention of "time", how about this answer. Ike rides from 12AM to 1AM on the spring night that Daylight Saving Time kicks in. Mike rides from 1AM to 2AM, but on this night 2AM becomes 3AM. Therefore Mike technically rode for two hours but covered the same distance.

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They both start at the end of the shadow, as they start at different times of day, this means that they are different distances from the spike. Therefore the terrain is different, Mike had a rugged or boggy terrain to cover so he covered less ground!

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My takeaway from the riddle is this

They use the same tricycle.

The peddal at the same rate.

they do this at 2 different times of the day.

I don't think that there is any trickery in the wording. Like it happens at 2am on daylight spending and we move the clock up an hour. BEcause that didn't take twice as long we just changed the clock.

Also the cover the same distance so doubleing the radius to get twice the circumference would in fact be double the distance.

That said I like the carosel I dea the best at on point in the day it would be turned on and one point it could be off. I just feel like the carosel answer is very ambiguous. because a similar result is achieved by one riding in one direction would and the other in the reverse. Also the timing of the speed of the carosel would have to be just perfect to achieve the timing described. Also technically speaking if the ground is rotaing under you then you are traveling twice as far in that ground measurement but from a diferent perspective you have only gone once around for example.

I am either over thinking this riddle or it is very clever because at a glance it looks simple.

Edited by Blavek
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Could this trike ...

... have gears, like a 10-speed bike? In that case, people in different gears could pedal at the same speed but cover different distances. The spike doesn't even have to come into play.

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So if you measure the distanc traveled in degrees they could circle at different radi and still travel 360degres. The person that is on the longer radius then would take longer to complete his 360 degrees. And if it was twice the short radius it should take twice as long. My issue here is degrees aren't a measure of distance.

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Mike and Ike buy a trike and ride in circles around a spike. They each ride at a different time of day. They both pedal at the same rate. They both make perfect circles with the spike at the exact center. Mike rides twice as long (time) as Ike, but they cover the exact same distance. How is this possible?

The wording in OP suggest that only one trike is purchased, which they use at different timings. It also suggests that the track is also the same. pedalling rate is also same. Then how is it possible that Mike pedals twice as long as Ike, and both covers same distance....?

It seems to be maths magic....! In my view if I am not wrong about the wordings in OP then it should be related to the pedal length. One pedal length by Ike may be equal to twice the length of one pedal by Mike.

This may be due to difference in their heights.

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Mike and Ike buy a trike and ride in circles around a spike. They each ride at a different time of day. They both pedal at the same rate. They both make perfect circles with the spike at the exact center. Mike rides twice as long (time) as Ike, but they cover the exact same distance. How is this possible?

The wording in OP suggest that only one trike is purchased, which they use at different timings. It also suggests that the track is also the same. pedalling rate is also same. Then how is it possible that Mike pedals twice as long as Ike, and both cover the same distance...?

This may be due to that one pedal by Ike covers the same distance as the distance covered by two pedals by Mike. so the lengths of Pedals are different and that is due to the difference of probably their heights.

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The heights of Mike and Ike may be different...!
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Different gear ratios

the wheels are changed for bigger or smaller wheels after each ride

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They both make perfect circles with the spike at the centre - Mike rides much closer to the spike, Ike rides further. The distance acts as the radius of the circle. One's circumference is twice of the others. The distance is the same as they both reach the start again - travelling 0 km.

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I've read all the comments so far and it looks like the solution os still elusive. Maybe we could have a ruling about gears and pedal length?

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Mike and Ike are determining their distance from the spike; the radius of the circuit of travel, by the length of the shadow cast by the spike at the different times of the day. Mikes rides near the middle of the day when the shadow is shorter, and Ike rides earlier or later when the shadow is longer.

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Mike and Ike buy a trike and ride in circles around a spike. They each ride at a different time of day. They both pedal at the same rate. They both make perfect circles with the spike at the exact center. Mike rides twice as long (time) as Ike, but they cover the exact same distance. How is this possible?

(Edit - minor change in terms)

The spike is on a boat in a river. When Mike rides the boat is going against the current. when Ike rides, it is going with the current.

Edited by Seltzer
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A change in gears?

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