SOLUTION: Hi 2 robots Jupiter and Mars competed in a race. The speed of Jupiter was 20cm/sec faster than Mars. When Jupiter crossed the finish line in 12 sec Mars only completed 2/3 of th

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Question 1169835: Hi
2 robots Jupiter and Mars competed in a race. The speed of Jupiter was 20cm/sec faster than Mars. When Jupiter crossed the finish line in 12 sec Mars only completed 2/3 of the race.
What was the distance of the race
Thanks
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the speed of the robot Mars, in cm/sec.

Then the speed of the robot Jupiter is (x+20) cm/sec.



The distance robot Jupiter traveled in 12 seconds is  12*(x+20)  cm.

The distance robot Mars    traveled in 12 seconds is  12*x  cm.


The condition says that Mars' distance is  2%2F3  of that of Jupiter

    12x = %282%2F3%29%2A12%2A%28x%2B20%29.


Simplify and solve


    12x = 8*(x+20)

    12x = 8x + 160

    12x - 8x = 160

       4x    = 160

        x = 160/4 = 40 cm/sec.


Thus the speed of the robot Mars is  40 cm/sec.

Hence, the speed of the robot Jupiter is  40+20 = 60 cm/sec.


Jupiter finished in 12 seconds - - - hence, the distance of the race was 60*12 = 720 cm = 7 m and 20 cm.    ANSWER

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


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.

let x = speed of Mars
then x+20 = speed of Jupiter

Mars's speed is 2/3 that of Jupiter's:

x%2F%28x%2B20%29+=+2%2F3

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.

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:

2%2F3+=+%282%2A20%29%2F%283%2A20%29+=+40%2F60+=+x%2F%28x%2B20%29

Mars's speed is 40cm/sec; Jupiter's is 60cm/sec.

Since Jupiter finished the race in 12 seconds, the length of the race was 12*60 = 720cm.