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Sagot :
Data:
Total distance: 450 miles
Total time: 8 h
Average 60 mi/h before noon
Average 50 mi/h afternoon
The relationship between the time, speed (average) and distance is drescribed in the next equations:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ d=s\times t \\ \\ \end{gathered}[/tex]Then, if you multiply the speed and the time you get the distance:
time before noon: b
time afternoon: a
[tex](60\times b)+(50\times a)=450[/tex]The sum of a and b is the total time:
[tex]a+b=8[/tex]Use the next system of equations to find a and b:
[tex]\begin{gathered} 60b+50a=450 \\ a+b=8 \end{gathered}[/tex]1. Solve a in the second equation:
[tex]\begin{gathered} \text{Subtract b in both sides of the equation:} \\ a+b-b=8-b \\ \\ a=8-b \end{gathered}[/tex]2. Substitute the a in first equation by the value you get in first step:
[tex]60b+50(8-b)=450[/tex]3. Solve b:
[tex]\begin{gathered} 60b+400-50b=450 \\ 10b+400=450 \\ \\ \text{Subtract 400 in both sides of the equation:} \\ 10b+400-400=450-400 \\ 10b=50 \\ \\ \text{Divide both sides of the equation into 10:} \\ \frac{10}{10}b=\frac{50}{10} \\ \\ b=5 \end{gathered}[/tex]4. Use the value of b=5 to solve a:
[tex]\begin{gathered} a=8-b \\ a=8-5 \\ a=3 \end{gathered}[/tex]Then, Jaron begin his trip 5 hours before noon ( at 7:00) and end it 3 hours afternoon (at 15:00)
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