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In a 24 km race, during which each runner maintains a constant speed throughout, Alice crosses the finish line while Becky is still 8 km from finishing and Caitlin is 12 km from finishing. When Becky crosses the finish line, Caitlin still has d kilometers to go. Find all possible values of d.

Respuesta :

Answer:6km

Step-by-step explanation:

Given

when Alice finishes the race Becky is 8km From finishing line

and caitlin 12 km from finishing line.

Suppose t is the time require by Alice to finish the race

and[tex] V_a,V_b,V_c[/tex] be the velocity of alice ,becky and caitlin

thus [tex]t=\frac{24}{V_a}=\frac{24-8}{V_b}=\frac{24-12}{V_c}[/tex]

thus [tex]\frac{V_b}{V_c}=\frac{4}{3}[/tex]

say t' is time required by beckey  to complete 8 km thus

[tex]V_b\times t'=8[/tex]

therefore for Caitlin

[tex]V_c\times t'=\frac{8}{V_b}\times V_c=6[/tex]

Thus caitlin will cover a distance of 6 km in t' time and 6 km away from finishing.

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