Revolutions - Wheel / Partial Solution

[Guest]

A bicycle is traveling at 10 mph. Diameter of wheels - 28 in. Determine number of revolutions the wheels make in per minute.

Let N = Number of revolutions

Circumference - pi * diameter

C - 3.1416 * 28 = 87.9648 = 88 in.

The wheel makes N revolutions per min.

In one min. the wheel travels pi * 28 * N in.

In one hr. the wheel travels pi * 28 * N * 60 in.

How do I proceed from here ?

[Guest]

You have found how far the bicycle travels in one revolution of the wheel, that is inches per revolution

You know the speed of the bicycle in miles per hour
You can convert this speed to inches per minute.

So it is easy now to get revolutions per minute

[Guest]

5280 feet = mile

5280 * 10 = 52800 feet in 10 miles.


52800 * 12 in. per foot = 633600 in. in 10 miles.

miles per hr. to in. per min. = 1 mph = 1056 in. per min. = 10 * 1056 = 10560

??

[Guest]

Is the last post meant to be a solution...?

[Guest]

"Is the last post meant to be a solution...?"

My attempt - Not sure.

[Guest]

In your first post you had got as far as calculating that the bicycle moved 88 inches for each revolution on the wheel......

I then outlined how to proceed from there......as is copied below.........

You have found how far the bicycle travels in one revolution of the wheel, that is inches per revolution

You know the speed of the bicycle in miles per hour.........this is given in the question
You can convert this speed to inches per minute. ........find this next or write an expression for this....

So it is easy now to get revolutions per minute .......find this from the 2 expressions from above

The numbers are so simple if you don't actually multiply them out at each stage you will find most of them cancel and leave a very simple answer................

[Guest]

"You know the speed of the bicycle in miles per hour.........this is given in the question
You can convert this speed to inches per minute. ........find this next or write an expression for this...."



Miles per hr. to in. per min. = 1 mph = 1056 in. per min. = 10 * 1056 = 10560


I don't know.

[Guest]

one mile per hour is 5280 feet per hour.................
and that is 12 x 5280 inches per hour............................
and that is 12 x 5280 / 60 inches per minute.....................
Now you know how many inches per minute if bicycle was moving at 1 mile per hour.............
But bicycle is moving at 10 miles per hour so it is 10 times that...................
So it is....... 10 x 12 x 5280 / 60 inches per minute for 10 miles per hour...........................

[Guest]

10 * 12 * 5280 / 60 = 10560

I have located the same problem in a different location with an answer of 120. How was that answer determined ?

[Guest]

So it is....... 10 x 12 x 5280 / 60 inches per minute for 10 miles per hour...........................

Do you read English language......................

The above calculation is not an answer to the problem...............
It clearly states in English that it is "inches per minute for bicycle travelling at 10 miles per hour"
And that works out at 10560 inches per minute.
But we are not asked for inches per minute. We are asked for revolutions per minute.
So something must be going around in circles........................

[Guest]

I misunderstood. My error. Thanks.

[Guest]

If 10560 and 120 is not the answer, I don't know. I'm sorry - I can't solve it.

[Guest]

When a bicycle moves ..... the things that go around in circles are its wheels..............

Do you want to know the answer OR do you want to know how to solve it.?

You had already worked out that 88 inches was the circumference of the wheel so in one revolution of the wheel it would roll 88 inches.

And the bicycle moves ....... 10 x 12 x 5280 / 60 inches per minute for travelling at 10 miles per hour ...........................

You seem to have ignored all advice that was given in the previous posts ......

You need to re-consider what you have worked out so far and how you can make further use of it or re-arrange it to obtain the answer requested.

How can you consider 10560 as the answer when its units are inches per minute and the question wants an answer as revolutions per minute

[Guest]

I will attempt again:

The wheels travel 88 inches in one revolution.

The bike is traveling at 10 mph.

5280 x10 = 52800 ft. * 12 in per ft. = 633600 in.

633600 / 88 = 7200

I don't know.

[Guest]

From your last attempt............

The wheels travel 88 inches in one revolution.

The bike is traveling at 10 mph. .....So bike travels 10 miles in one hour.....

5280 x10 = 52800 ft. * 12 in per ft. = 633600 in. ......So this is the inches in the 10 miles travelled in one hour

633600 / 88 = 7200 ......So this is the inches in 10 miles(per 1 hour) divided by inches in one revolution.

So we have.....( Inches per hour) / (inches per revolution) ......So that is revolutions in one hour

If you had 1000 marbles in boxes of 10 in each box you would have 1000 / 10 = 100 boxes.

[Guest]

7200 revolutions per hr. / 60 min. per hr. = 120 revolutions per min.

[Guest]

So....You see it was just another Simple sum..................

[Guest]

Yes - Thanks.