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# HELP with math homework

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5) Natalie was running a race with her friend. Natalie’s friend ran 23 miles of the race. Natalie ran 12 mph slower than her friend. If Natalie’s friend ran the race in 3 hours, and 12 minutes, how fast did Natalie run the race?

Guest Mar 4, 2017
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3hr, 12minutes  =   3.2 hrs

And   Distance  / Time  = Rate....so

23miles / 3.2hours     =  7.1875 mph  =  rate of Natalie's friend

Thus....it's impossible that Natalie ran 12mph slower than this  !!!!!

CPhill  Mar 5, 2017
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I think when you say "12mph slower", I believe you mean "12 miles slower than her friend over the same distance of 23 miles"??!!. If so, then it means that when her friend finished the 23-mile run, Natalie was still 12 miles from the finish line. Therefore, Natalie's speed was:[23 - 12] / 3.2 hours =3.4375 mph. Then,the time it takes Natalie to finish the race would be:

23 / 3.4375 =6.69 hours, or about 6 hours and 41.4 minutes.

Guest Mar 5, 2017
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Natalie was running a race with her friend. Natalie’s friend ran 23 miles of the race. Natalie ran 1.2 mph slower than her friend. If Natalie’s friend ran the race in 3 hours, and 12 minutes, how fast did Natalie run the race?

$$v_F=\frac{23miles}{3\frac{12}{60}h}=7.1875\ miles/h$$

$$v_N=7.1875\ mph-1.2\ mph=5.9875\ mph$$

$$t_N=\frac{s}{v_N}=\frac{23miles}{5.9857mph}=3h\ 50min\ 28.81sec$$

$$Natalie \ run \ the \ race \ in \ 3h\ 50min\ 28.81sec.$$

!

asinus  Mar 5, 2017
edited by asinus  Mar 5, 2017