The front wheel of a tricycle has a circumference of 63 inches, and the back wheels have a circumference of36 inches. If points P and Q are both touch

permaneceerc 2021-06-19 Answered
The front wheel of a tricycle has a circumference of 63 ​inches, and the back wheels have a circumference of36 inches. If points P and Q are both touching the sidewalk when Felicity starts to​ ride, how far will she have ridden when P and Q first touch the sidewalk at the same time​ again?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

SabadisO
Answered 2021-06-20 Author has 26472 answers

The circumference of the front wheel is \(\displaystyle{2}\cdot{63}\cdotπ={126}π\) inches and of the back wheel is \(\displaystyle{2}\cdot{36}\cdotπ={72}π\) inches. Therefore if the front wheel does m full turns, for m a natural number, the tricycle moves \(\displaystyle{m}\cdot{126}π\) inches, and if the back wheel does n full turns the tricycle moved \(\displaystyleπ\cdot{72}π\).
The points P and Q then touch the sidewalk at the same time for m and n such that \(\displaystyle{m}\cdot{126}π={n}\cdot{72}π\), which is equivalent, by dividing both sides by \(18 \pi\), to \(\displaystyle{m}\cdot{7}=π\cdot{4}\), Since the minimal common multiple of 7 and 4 is 25 we have that the smallest m and n satisfying this equations are \(m = 4\) and \(n=7\).
Therefore Felicity will have ridden \(\displaystyle{4}\cdot{126}π={504}π\) inches when P and Q frst touch the sidewalk at the same time.

Not exactly what you’re looking for?
Ask My Question
33
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-10
Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it’s not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.
asked 2021-05-12
4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy?
b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
asked 2021-06-18
A bicycle tire has a diameter of 27 inches. How far does the bike travel along the ground when the wheel rotates once?
asked 2021-03-22
A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?
asked 2021-03-24
The flywheel of a punch press has a moment of inertia of \(\displaystyle{16.0}{k}{g}\cdot{m}^{{2}}\) and runs at 300 rev/min. The flywheel supplies all theenergy needed in a quick punching operation.
a)Find the speed in rev/min to which the fly wheel will be reducedby a sudden punching operation requiring 4000J of work.
b)What must the constant power supply to the flywheel (in watts) beto bring it back to it's initial speed in a time of 5.00 s?
asked 2021-04-03
A wheel is rotating freely at angular speed 800 rev/min on ashaft whose rotational inertia is negligible. A secod wheel,initially rest and with twice the rotational inertia of the first,is suddenly coupled to the same shaft.
A) what is the angular speedof the resultant combination of the shaft and the two wheels?
B)What fraction of the orginial rotational kinetic energy is lost?
asked 2021-02-26
The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, If the string is pressed down at this fret and plucked, what is the new fundamental frequency? The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one sixth of the way along its length from the bridge. What frequency will be heard then?

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question
...