Lana completed a 10-mile race in 90 minutes. She ran most of it, but she also walked a little bit. She knows that she usually runs at a pace of 8.5 minutes per mile and she usually walks at a pace of 12 minutes per mile. Assuming that she kept these times during the periods of running and walking during her 10-mile race, how many minutes did she spend running and how many minutes did she spend walking?

Question

26-01-2019
Mathematics

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Lana completed a 10-mile race in 90 minutes. She ran most of it, but she also walked a little bit. She knows that she usually runs at a pace of 8.5 minutes per mile and she usually walks at a pace of 12 minutes per mile. Assuming that she kept these times during the periods of running and walking during her 10-mile race, how many minutes did she spend running and how many minutes did she spend walking?

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ColinJacobus ColinJacobus · Answer 1 · 2019-02-04T08:09:06+01:00

Answer: The answers are [tex]72\dfrac{6}{7},~~17\dfrac{1}{7}~\textup{minutes}.[/tex]

Step-by-step explanation: Given in the question that Lana completed a 10-mile race in 90 minutes by running and walking both. She usually runs at a pace of 8.5 minutes per mile and walks at a pace of 12 minutes per mile. We need to find the number of minutes for which she ran and walk throughout the race.

Let, Lana runs for 'x' miles and walks for 'y' miles. Then, we have

[tex]x+y=10\\\\8.5x+12y=90.[/tex]

Multiplying the first equation by 8.5 and subtracting from the second equation, we have

[tex]12y-8.5y=90-85\\\\\Rightarrow 3.5y=5\\\\\Rightarrow y=\dfrac{5}{3.5}\\\\\Rightarrow y=\dfrac{10}{7}.[/tex]

Therefore,

[tex]x=10-\dfrac{10}{7}=\dfrac{60}{7}.[/tex]

Thus, time for which Lana ran is

[tex]\dfrac{60}{7}\times 8.5=\dfrac{510}{7}=72\dfrac{6}{7}~\textup{minutes}.[/tex]

And, the time for which Lana walks is

[tex]\dfrac{10}{7}\times 12=\dfrac{120}{7}=17\dfrac{1}{7}~\textup{minutes}.[/tex]

Thus, the answers are

[tex]72\dfrac{6}{7},~~17\dfrac{1}{7}~\textup{minutes}.[/tex]