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Math Question

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The inhabitants of the planet Rundia can run footraces similar to those run on Earth. However, Rundians measure the distances they run in bars, where one bar measures $$\frac{4}{5}$$of a meter, and they measure time in ticks, where there are 100 ticks in one minute. Rundian sprinter Sejes Wesno can run a 100-bar race in 11.53 ticks. The great Earth sprinter Usain Bolt ran a 100-meter race in 9.58 seconds. If Wesno is k times as fast as Bolt, what is the value of k? Round to nearest hundredth.

Nov 21, 2018
edited by dgfgrafgdfge111  Nov 22, 2018
edited by dgfgrafgdfge111  Nov 22, 2018

#1
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Does Sejes run 100 bar race in 9.58 seconds.....or 9.58 ticks?

Nov 22, 2018
#2
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Oh, I'm really sorry, I meant ticks. I typed it wrong.

dgfgrafgdfge111  Nov 22, 2018
#3
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OK.....going to do some conversions into the metric system

11.58 ticks / 100 ticks/min x 60 sec/min =6.948 sec seconds

100 bar x 4/5 m/bar = 80 meters       His RATE is   80 meters/6.948sec = 11.514m/s

Usain rate = 100m/9.58sec = 10.43 m/s

So       10.43k = 11.514     k = 1.10

OK....the question was changed after I posted my answer   9.58 ticks was changed to 11.58 ticks

changed my answer to reflect new numbers

Nov 22, 2018
edited by ElectricPavlov  Nov 22, 2018
#4
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The answer is actually 1.11, but I don't know how.

dgfgrafgdfge111  Nov 22, 2018
#5
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I get k = 1.33 using the data provided in the question.  In order to get k = 1.11 I have to assume that Bolt runs 100 m in 9.85 s and Wesno runs 100 bars in 11.85 ticks!

Nov 22, 2018
#7
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Oh, I see. There must have been a mistake!

dgfgrafgdfge111  Nov 22, 2018
#6
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Wait, it is 1.30 seconds!

Since 1 bar is 4/5 of a meter, then 100 bars would be 80 meters. And, since there are 100 ticks in a minute and Sejes runs for 9.58 ticks, that is actually 5.75 seconds. So, he runs 80 meters in 5.75 seconds. On the other hand, Usain Bolt runs 1000 meters in 9.58 seconds. Thus, multiplying each side by 1.25, we get 5.75*1.25=7.1875 seconds. Now, divide 9.58 by 7,1875 to get approximately 1.33. Rounding that to the nearest hundredth gives us 1.30!

Nov 22, 2018
#8
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Alan's calculation is exactly 1 1/3. If you have to round it to the 100th decimal place, then it becomes 1.33.

Nov 22, 2018