Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
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 appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
