Question

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.

Answer 1

Answer:6km

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
`V_a,V_b,V_c` be the velocity of alice ,becky and caitlin

thus
`t=(24)/(V_a)=(24-8)/(V_b)=(24-12)/(V_c)`

thus
`(V_b)/(V_c)=(4)/(3)`

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

`V_b* t'=8`

therefore for Caitlin

`V_c* t'=(8)/(V_b)* V_c=6`

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