SOLUTION: Three motorists A, B and C often travel on a certain highway, and each motorist always travels at a constant speed. A is the fastest of the three and C the slowest. One day, wh

Question 232410: Three motorists A, B and C often travel on a certain highway, and each motorist always travels at a constant speed. A is the fastest of the three and C the slowest.
One day, when the three travel in the same direction, B overtakes C, five minutes later, A overtakes C and in another 3 minutes, A overtakes B. On another occasion when they again travel in the same direction, A overtakes B first, then, nine minutes later, A overtakes C. When will B overtake C?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
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
--------------------------------------------------------------------
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)
-------------------------------------------------------
Let = C's time for last part of 2nd trip (B overtakes C)
Using the 1st ratio:

min
---------------------
Using the 2nd ratio:

min
B will overtake C in 15 min
and
Plugging back into the ratios, I get

and

Both are true