# calculating true odometer reading from inaccurate speedometer

I'm very poor with math and hoping someone can help me with a question.

The odometer is reading 8000km but it's reading speed incorrectly and logging the speedo speed to the odometer. For KMs 2000-6000 it's logging at 18kmph over, and 6000-7000 is logging 10kmph over. What is the accurate reading it should be showing?

More details:

If a motorcycle travels:

6000km with the speedometer reading 18kmph over actual speed (50kmph reads 68kmph roughly)

1000km with the speedometer reading 10kmph over actual speed. (50kmph reads 60kmph roughly)

How many actual kilometers were traveled?

I don't know how to phrase this question to look up an answer online.

If I can do it by % change the sprocket ratios are:

13/43 for 1000km

13/50 for 6000km

14/50 for 1000km

Would I calculate the % increase in kmph from the actual kmph to the indicated kmph and then subtract that from the indicated odometer reading (for 1k,6k,1k)? If I'm traveling 30% slower than indicated can I just subtract 30% of the total odometer reading (km) for that time frame when I was running whatever gear ratio?

Thanks to anyone who wants to help! I know this isn't a challenging question in the slightest to a lot of you here but I'm not sure where else to ask for proper help.

Thanks so much! If there is a more relevant place to post please let me know. Also this isn't a elementary textbook question I'm just putting on a new speedometer unit for my dualsport, haha.

• If the motorcycle travels $1000$ km, $6000$ km, and $1000$ km, doesn't it actually travel $8000$ km? What does it matter what the speedometer reads? Feb 15, 2021 at 19:26
• Sorry, I didn't phrase it very well. I meant to say the odometer is reading 8000km but it's reading speed incorrectly and logging the speedo speed to the odometer. For KMs 2000-6000 it's logging at 18kmph over, and 6000-7000 is logging 10kmph over. Feb 15, 2021 at 19:32
• Thanks for the clarification. Please edit your question. Since you're new to the site, let me explain that the goal is for questions to stand on their own; people shouldn't have to read the comments to understand. Welcome to MSE. Feb 15, 2021 at 19:39
• Edited! Thank you! Feb 15, 2021 at 20:31

All of these scenarios fit the information given. Ignoring the constraint of physical plausibility, the bike could have travelled any distance between $$0$$ and $$5000$$ km during the middle stretch, and similarly, the bike could have travelled any distance between $$0$$ and $$1000$$ km during the final stretch.