The speed of an object is the rate of distance traveled over time. Suzette ran for 1.5 hours, and she biked for 2 hours.
Given that:
[tex]Distance = 34mi[/tex]
[tex]Time = 3.5h[/tex]
Speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
Make Distance the subject
[tex]Distance = Speed \times Time[/tex]
Average running speed = 6 mph for x hours implies that:
[tex]Distance = 6 \times x[/tex]
[tex]Distance = 6x[/tex]
Average biking speed = 12.5 mph for y hours implies that:
[tex]Distance = 12.5 \times y[/tex]
[tex]Distance = 12.5y[/tex]
So, the total distance is:
[tex]Total = 6x + 12.5y[/tex]
The total distance is 34 miles. So, we have:
[tex]6x + 12.5y = 34[/tex]
The total time is 3.5h. So, we have:
[tex]x + y = 3.5[/tex]
Make x the subject
[tex]x = 3.5 - y[/tex]
Substitute [tex]x = 3.5 - y[/tex] in [tex]6x + 12.5y = 34[/tex]
[tex]6(3.5 - y) + 12.5y = 34[/tex]
[tex]21 - 6y + 12.5y = 34[/tex]
Collect like terms
[tex]- 6y + 12.5y = 34 - 21[/tex]
[tex]6.5y = 13[/tex]
Divide both sides by 6.5
[tex]y = 2[/tex]
Recall that:
[tex]x = 3.5 - y[/tex]
[tex]x = 3.5 - 2[/tex]
[tex]x = 1.5[/tex]
Hence, Suzette ran for 1.5 hours, and she biked for 2 hours.
Read more about speed at:
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