Asked by XXX
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.
Answers
Answered by
Reiny
Suppose it took Alice 4 hrs, when she finished
Alice went at 6 km/h
Becky went 16 km at 4 km/h
Caitlin went 12 km at 3 km/h
So for Becky to finish her remaining 8 km would take an extra 2 hrs, but in 2 hrs Caitlin only went 6 more km of her remaining 12 km, so she still has 6 km to go , d = 6
suppose Alice took 5 hrs.
Alice's rate = 24/5 or 4.8 km/h
Becky's rate = 16/5 or 3.2 km/h
Cailin's rate = 12/5 = 2.4 km/h
So for Becky to finish her remaining 8 km would take an extra 2.5 hrs, but in 2.5 hrs Caitlin only went 6 more km of her remaining 12 km, so she still has 6 km to go , d = 6
Suppose Alice took t hrs
Alice went 24 km , her rate is 24/t km/h
Becky went 16 km , her rate is 16/t km/h
Caitlin went 12 km , her rate is 12/t km/h
So for Becky to finish her remaining 8 km would take an extra 8÷(16/t) or t/2 hrs, but in t/2 hrs Caitlin only went (t/2)(12/t) or 6 more km of her remaining 12 km, so she still has 6 km to go , d = 6
Ahhh, d = 6
Alice went at 6 km/h
Becky went 16 km at 4 km/h
Caitlin went 12 km at 3 km/h
So for Becky to finish her remaining 8 km would take an extra 2 hrs, but in 2 hrs Caitlin only went 6 more km of her remaining 12 km, so she still has 6 km to go , d = 6
suppose Alice took 5 hrs.
Alice's rate = 24/5 or 4.8 km/h
Becky's rate = 16/5 or 3.2 km/h
Cailin's rate = 12/5 = 2.4 km/h
So for Becky to finish her remaining 8 km would take an extra 2.5 hrs, but in 2.5 hrs Caitlin only went 6 more km of her remaining 12 km, so she still has 6 km to go , d = 6
Suppose Alice took t hrs
Alice went 24 km , her rate is 24/t km/h
Becky went 16 km , her rate is 16/t km/h
Caitlin went 12 km , her rate is 12/t km/h
So for Becky to finish her remaining 8 km would take an extra 8÷(16/t) or t/2 hrs, but in t/2 hrs Caitlin only went (t/2)(12/t) or 6 more km of her remaining 12 km, so she still has 6 km to go , d = 6
Ahhh, d = 6
Answered by
Jon
Please no AoPS problems!
Answered by
aops cop
I am a AoPs worker and you shouldn't be googling Algebra A question online. I must tell you.
Answered by
Wonka
Busted!
Answered by
TK24NC
Excuse me. If you are an AoPs worker, you wouldn't go and post that online trying to make it obvious.
Answered by
AoPSSheriff
@all above, please refrain from searching for answers to the class, "Introduction to Algebra A".
Answered by
AoPS person
we;; mp
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.