Question 232410
I tried to extract the information that
would lead to a solution.
(a) In both trips, B is the only one that starts and finishes
(b) Nothing is known about speeds or distances, only times
(c) For the 1st trip, C travels for 5 min, then A travels for 3 min
(d) For the 2nd trip, A travels for 9 min, then C travels for ? min
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I set up this ratio:
(A's time on 1st trip) / (time for 1st trip which is B's time) = 
(A's time on 2nd trip) / (time for 2nd trip which is B's time)
And I could have used this ratio, too:
(C's time on 1st trip) / (time for 1st trip which is B's time) = 
(C's time on 2nd trip) / (time for 2nd trip which is B's time)
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Let {{{C}}} = C's time for last part of 2nd trip (B overtakes C) 
Using the 1st ratio:
{{{3/8 = 9/(9 + C)}}}
{{{3*(9 + C) = 72}}}
{{{27 + 3C = 72}}}
{{{3C = 45}}}
{{{C = 15}}} min
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Using the 2nd ratio:
{{{5/8 = C/(9 + C)}}}
{{{8C = 5*(9+C)}}}
{{{8C = 45 + 5C}}}
{{{3C = 45}}}
{{{C = 15}}} min
B will overtake C in 15 min
and
Plugging {{{C = 15}}} back into the ratios, I get
{{{3/8 = 9/24}}}
and
{{{5/8 = 15/24}}}
Both are true