Word problem: Given that speedometer is off by 5mph, find error in odometer reading.

ammelton1990

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I do not know how to start to solve this.

My car speedometer measures 5 MPH more than the speed at which I am actually traveling. If my car registers that I travel 10,000 miles in one year, how many miles have I actually traveled?
 
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My car speedometer measures 5 MPH more than the speed at which I am actually traveling. If my car registers that I travel 10,000 miles in one year, how many miles have I actually traveled?
What are your thoughts?

Please share your work with us ...even if you know it is wrong.

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Ok, so if the car registers 10,000 miles. Then I will have traveled 200 hours.

Is that right?
 
I honestly don't have a clue
how to do this.. is there a formula?
I don't understand how the amount of hours I have driven factors into this.
 
I do not know how to start to solve this.

My car speedometer measures 5 MPH more than the speed at which I am actually traveling. If my car registers that I travel 10,000 miles in one year, how many miles have I actually traveled?
First I doubt that your speed (and hence odometer) is exactly 5 mph over all the time. Usually it is off by a percentage. That is the faster you go, then the larger the error.

But let's assume that your premise is correct. Then I maintain that you can't do this problem.
For suppose you always drive your car at 1,000 mph and therefore drive for only 10 hours, then your odometer is off my 10*5 or 50 miles.

Now suppose that you drive your car much slower, then the number of hours you drive will be more than 10 hours and hence have a (much) larger error.

At idle, your speedometer will read 5 miles per hour. After it reaches 10,000 miles after the year (at idle!), then the error will be 10,000 miles as your car never moved.
 
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First I doubt that your speed (and hence odometer) is exactly 5 mph over all the time. Usually it is off by a percentage. That is the faster you go, then the larger the error.

But let's assume that your premise is correct. Then I maintain that you can't do this problem.
For suppose you always drive your car at 1,000 mph and therefore drive for only 10 hours, then your odometer is off my 10*5 or 50 miles.

Now suppose that you drive your car much slower, then the number of hours you drive will be more than 10 hours and hence have a (much) larger error.

At idle, your speedometer will read 5 miles per hour. After it reaches 10,000 miles after the year (at idle!), then the error will be 10,000 miles as your car never moved.

How do I figure out how many extra miles are on my car?
 
How do I figure out how many extra miles are on my car?
It sounds like you're expecting an answer. But the replies you've received have explained, quite nicely, that this exercise is not answerable as posted.

Even were the speedometer always "off" by a set amount, that has little to nothing to do with the odometer reading. So knowing that the speedometer is wrong tells us nothing about the odometer -- or the tachometer, or the dash clock, or anything else!

Please reply with the full and exact text of the exercise, the complete instructions, any related information (tables, formulas, graphics, etc), and a clear listing of your thoughts and efforts so far. Thank you! ;)
 
How do I figure out how many extra miles are on my car?
As I said, how much your odometer is off by depends on your (average) speed. Just re-read my post. It clearly tells how much your odometer will be off at various speeds.

And please stop asking us to do your work for you. This is a math help website.
 
I do not know how to start to solve this.

My car speedometer measures 5 MPH more than the speed at which I am actually traveling. If my car registers that I travel 10,000 miles in one year, how many miles have I actually traveled?

Clearly this is not a class exercise, as it would be nonsense. So let's just make a guess as to the reality, and work things out.

Suppose the speedometer reads 45 when you are going 40. If this is caused by something like a wrong sized tire, that would mean the speed is always reading 45/40 = 9/8 times the actual speed; and the odometer would always read 9/8 times the actual distance. If your odometer added 10,000 miles, how many miles did you really go? I'll leave that much for you to do; but you'll have to decide what your speed is when it's 5 mph over.

If you are right that the speedometer always reads 5 mph over the actual speed, even when you are not moving (so that in park it reads 5 mph), then the problem has to be in the speedometer dial or display or whatever your car has. It doesn't affect the odometer at all; you drove 10,000 miles. (If it did affect the odometer, the odometer would be turning while you are parked, and you'd be asking your mechanic why the car is haunted, rather than asking us how far you drove!)

I can't think of any other options. Any thoughts?

In the future, please respond to questions you are asked, rather than ignoring what everyone tells you.
 
Thank you all for responding, especially Dr. Peterson. I am sorry I took so long to respond. I truly appreciate all of you. Thanks for taking the time to try to help me. I still don't understand how to figure how many extra miles my car may have registered, if any, or if it is even possible to determine. I get that some of you may think that I am just looking for an answer, maybe even lazy, or that I am not willing to do the work. That is not the case. I sincerely do not understand. I don't get it..but thank you.. All of you!!
--Also, I bought new tires, Thank You again Dr. Peterson, that fixed the problem.
 
Thank you all for responding, especially Dr. Peterson. I am sorry I took so long to respond. I truly appreciate all of you. Thanks for taking the time to try to help me. I still don't understand how to figure how many extra miles my car may have registered, if any, or if it is even possible to determine. I get that some of you may think that I am just looking for an answer, maybe even lazy, or that I am not willing to do the work. That is not the case. I sincerely do not understand. I don't get it..but thank you.. All of you!!
--Also, I bought new tires, Thank You again Dr. Peterson, that fixed the problem.

It would be possible to answer your question if you filled in one gap: what speed were you going when the speedometer read 5 mph over? At one point I supposed it was 40, and showed most of the resulting work:
Suppose the speedometer reads 45 when you are going 40. If this is caused by something like a wrong sized tire, that would mean the speed is always reading 45/40 = 9/8 times the actual speed; and the odometer would always read 9/8 times the actual distance. If your odometer added 10,000 miles, how many miles did you really go? I'll leave that much for you to do; but you'll have to decide what your speed is when it's 5 mph over.
The answer in this case is the that actual distance would be 8/9 of what the odometer said: 8/9 * 10,000 = 8889 miles. So the odometer showed 1111 extra miles.
 
It would be possible to answer your question if you filled in one gap: what speed were you going when the speedometer read 5 mph over? At one point I supposed it was 40, and showed most of the resulting work:

The answer in this case is the that actual distance would be 8/9 of what the odometer said: 8/9 * 10,000 = 8889 miles. So the odometer showed 1111 extra miles.


It read 5 miles more from 30 to 50. I was not able to check it at higher speeds. I first noticed that it was wrong at 45.

How did you know to start this problem? I understand 45/40. Actual speed over the speed that the odometer is reading.
Why did you use 8/9 instead of 9/8 When you multiplied by 10000?
 
It read 5 miles more from 30 to 50. I was not able to check it at higher speeds. I first noticed that it was wrong at 45.

How did you know to start this problem? I understand 45/40. Actual speed over the speed that the odometer is reading.
Why did you use 8/9 instead of 9/8 When you multiplied by 10000?

OK. If I am right that the error is really proportional, it would not be off by exactly the same amount over this entire range; but if it was off by 5 at 40 (readying 45), then it is high by 1/9, or 11.1%. That means it would read 33.75 at 30 (high by about 4), and 56.25 at 50 (high by about 6). Let's suppose that you thought of these as "about 5 mph high" over that entire range. Then we can take my supposition as the approximate reality. We already have the answer.

So here's the reasoning behind the math: if we have

speedometer speed = (9/8) * actual speed

then the same is true of distance:

odometer distance = (9/8) * actual distance.

You want to solve for the actual distance, so we multiply both sides by the reciprocal, 8/9. You could also think of this as undoing the multiplication by 9/8, by dividing by 9/8 (which is the same as multiplying by 8/9). So we have

actual distance = (8/9) * odometer distance
 
OK. If I am right that the error is really proportional, it would not be off by exactly the same amount over this entire range; but if it was off by 5 at 40 (readying 45), then it is high by 1/9, or 11.1%. That means it would read 33.75 at 30 (high by about 4), and 56.25 at 50 (high by about 6). Let's suppose that you thought of these as "about 5 mph high" over that entire range. Then we can take my supposition as the approximate reality. We already have the answer.

So here's the reasoning behind the math: if we have

speedometer speed = (9/8) * actual speed

then the same is true of distance:

odometer distance = (9/8) * actual distance.

You want to solve for the actual distance, so we multiply both sides by the reciprocal, 8/9. You could also think of this as undoing the multiplication by 9/8, by dividing by 9/8 (which is the same as multiplying by 8/9). So we have

actual distance = (8/9) * odometer distance

Thank you!! Seriously.. Thank you for explaining it.
 
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