Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Given:
Total time spends = 3 hours
Distance covered by bik = 3 miles
Distance covered by Jogging = 5 miles.
Her rate for jogging was 4 mph less than her biking rate.
Required- her rate when jogging.
Explanation:
Let her rate when jogging be x mph.
Given that her rate for jogging was 4 mph less than her biking rate.
So, her rate when biking will be:
[tex]\begin{gathered} Rate\text{ when jogging =Rate of biking -4} \\ x=Rate\text{ of biking -4} \\ Rate\text{ of biking =}(x+4)mph \end{gathered}[/tex]Now, the formula for the distance is:
[tex]\begin{gathered} \text{ Distance=Rate}\times time \\ \\ \Rightarrow Time=\frac{Distance}{Rate} \end{gathered}[/tex]The total time spend is 3 hours. So, we have the equation:
[tex]\begin{gathered} Time\text{ take by biking+Time take by jogging=total time} \\ \\ \frac{Distance\text{ covered by biking}}{Rate\text{ of biking}}+\frac{Distance\text{ covered by jogging}}{Rate\text{ of jogging}}=3\text{ hours} \\ \\ \frac{3}{x+4}+\frac{5}{x}=3 \end{gathered}[/tex]Solving further, we have:
[tex]\begin{gathered} \frac{3x+5(x+4)}{x(x+4)}=3 \\ \\ 3x+5x+20=3x(x+4) \\ \\ 8x+20=3x^2+12x \\ \\ 3x^2+12x-8x-20=0 \\ \\ 3x^2+4x-20=0 \end{gathered}[/tex]Now, solving the quadratic equation.
[tex]\begin{gathered} 3x^2+4x-20=0 \\ \\ 3x^2-6x+10x-20=0 \\ \\ 3x(x-2)+10(x-2)=0 \\ \\ (x-2)(3x+10)=0 \end{gathered}[/tex]Now, we find the value of x by equating the factors by zero.
[tex]\begin{gathered} x-2=0 \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} 3x+10=0 \\ 3x=-10 \\ x=\frac{-10}{3} \end{gathered}[/tex]Here, x=2 and -10/3.
We know that the rate cannot be in negative. So, we neglect the negative value of x.
Taking x=2 into account.
So, her rate when jogging is 2mph.
Final answer: Her rate when jogging is 2 mph.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.