Question 1169835
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The given information compares the distances that the two robots traveled in the same amount of time.  So the ratio of distances is the same as the ratio of speeds.<br>
let x = speed of Mars
then x+20 = speed of Jupiter<br>
Mars's speed is 2/3 that of Jupiter's:<br>
{{{x/(x+20) = 2/3}}}<br>
We could of course solve that algebraically.  However, we can get the answer perhaps a bit faster by thinking in terms of writing the fraction 2/3 as an equivalent fraction in which the denominator is 20 more than the numerator.<br>
In the fraction 2/3, the difference between numerator and denominator is 1, so we will get the desired fraction by multiplying numerator and denominator by 20:<br>
{{{2/3 = (2*20)/(3*20) = 40/60 = x/(x+20)}}}<br>
Mars's speed is 40cm/sec; Jupiter's is 60cm/sec.<br>
Since Jupiter finished the race in 12 seconds, the length of the race was 12*60 = 720cm.<br>