In a race, the second place finisher crossed the finish line 2 1/5 minutes behind the second place finisher took 39 2/3 minutes. how long did the winner take?

37 7/15 minutes

Step-by-step explanation:

The winner took 2 1/5 minutes less than the 39 2/3 minutes taken by the second place finisher. That time is ...

... 39 2/3 - 2 1/5 = (39 -2) + (2/3 -1/5) = 37 + (5·2 -3·1)/(3·5)

... = 37 7/15 . . . . minutes

It might be easier to compute the time in minutes and seconds.

... 39 2/3 minutes = 39 minutes 40 seconds

... 2 1/5 minutes = 2 minutes 12 seconds

Then the difference is ...

... (39 -2) minutes (40 -12) seconds = 37 minutes 28 seconds

Adding fractions

The sum of fractions a/b and c/d can be found as ...

... a/b + c/d = (ad +bc)/(bd)

For a=2, b=3, c=-1, d=5, the sum is (2·5+3·(-1))/(3·5) = (10-3)/15 = 7/15

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Time conversions

A minute is 60 seconds, so the number of seconds in a fraction of a minute is found by multiplying that fraction by 60 seconds.

... 2/3 × 60 seconds = 40 seconds

... 1/5 × 60 seconds = 12 seconds

... 7/15 × 60 seconds = 28 seconds

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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