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

#1**0 **

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

#2**0 **

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

#3**0 **

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