The Average Speed

Algebra Level 3

Damar has just got a new bike. It has a speedometer which sits on the handlebar. The speedometer can tell Damar the distance he travels and his average speed for a trip. Damar rode her bike from home to the river, which is 5 km away. It took him 75 minutes. He rode home using a shorter route of 4 km. This only took him 40 minutes. What was Damar’s average speed, in km/h, for the trip to the river and back?


The answer is 4.8.

Achmad Damanhuri by Achmad Damanhuri , 26, Indonesia

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2 solutions

Achmad Damanhuri
Sep 13, 2018

first he traveled in v 1 = 5 75 k m / m i n u t e v_1=\frac{5}{75}km/minute then v 2 = 4 40 k m / m i n u t e v_2=\frac{4}{40}km/minute the average time he traveled is using harmonic mean v a v e r a g e = 2 1 1 / 15 + 1 1 / 10 v_{average}=\frac{2}{\frac{1}{1/15}+\frac{1}{1/10}} v a v e r a g e = 2 25 k m / m i n u t e = 60 × 2 5 k m / h o u r v_{average}=\frac{2}{25}km/minute=60\times\frac{2}{5}km/hour then we get v a v e r a g e = 4.8 k m h − 1 v_{average}=4.8kmh^{-1}

from what i know this prob hould be calculated by harmonic mean (please correct me if im wrong) and sorry for the previous (there's an error)

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He takes 12 minutes for 4 km, and then 6 minutes for 3 km, so he traveled 7 km in 18 minutes, which is an average speed of 7/18*60=23.333... You can also see this if you calculate the speeds: 12 minutes for 4 km is an average speed of 20 km/h, and 6 minutes for 3 km is an average speed of 30 km/h, so the overall average has to be number in between!

Maurice van Peursem - 2 years, 9 months ago

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sorry i made a mistake in the previous post, but from what i know. we should use harmonic mean

Achmad Damanhuri - 2 years, 8 months ago

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My answer was correct, but now you have changed the question so your (at first incorrect) answer is suddenly correct. I don't think that is fair!!!

Maurice van Peursem - 2 years, 8 months ago

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@Maurice van Peursem – no, your answer is wrong even though there is no error in my question in the first place. the point is when we deal with average speed we use harmonic mean

Achmad Damanhuri - 2 years, 8 months ago
Jon Haussmann
Sep 17, 2018

"Damar has just got a new bike. It has a speedometer which sits on the handlebar. The speedometer can tell Damar the distance he travels and his average speed for a trip. Damar rode her bike from home to the river, which is 5 km away. It took him 75 minutes. He rode home using a shorter route of 4 km. This only took him 40 minutes. What was Damar’s average speed, in km/h, for the trip to the river and back?"

The average speed is 5 + 4 75 60 + 40 60 = 108 23 ≈ 4.696. \frac{5 + 4}{\frac{75}{60} + \frac{40}{60}} = \frac{108}{23} \approx 4.696.

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i think we should read this https://brilliant.org/wiki/harmonic-mean/ http://www.statisticshowto.com/harmonic-mean/

Achmad Damanhuri - 2 years, 8 months ago

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I think you should review what "average speed" means.

Jon Haussmann - 2 years, 8 months ago

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