parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?
A. 21
B. 23
C. 42
D. 46
E. 483
Before solving the question, let's make sure we fully understand what the question tells us AND the implications. Given: Candice can complete one lap in 42 seconds. So, after 42 seconds, Candice will be at the starting point (and she will have completed
1 lap).
After 84 seconds, Candice will be at the starting point (and she will have completed
2 laps).
After 126 seconds, Candice will be at the starting point (and she will have completed
3 laps).
After 168 seconds, Candice will be at the starting point (and she will have completed
4 laps).
etc...
If we let
C = the number of laps Candice has completed, then
42C = Candice's
total running timeGiven: Sabrina can complete one lap in 46 seconds. So, after 46 seconds, Sabrina will be at the starting point (and she will have completed
1 lap).
After 92 seconds, Sabrina will be at the starting point (and she will have completed
2 laps).
After 138 seconds, Sabrina will be at the starting point (and she will have completed
3 laps).
After 184 seconds, Sabrina will be at the starting point (and she will have completed
4 laps).
etc...
If we let
S = the number of laps Sabrina has completed, then
46S = Sabrina's
total running timeHow many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?If Candice and Sabrina were
together at the starting point, then we know that :
42C =
46SAside: Keep in mind that, in order for both people to be at the
starting point,
C and
S must both be positive
integersSo, we're looking for the smallest possible integer value of
C such that:
42C =
46STo make things a bit easier on ourselves, let's divide both sides of the equation by 2 to get:
21C = 23SAt this point, we can see that the smallest possible (positive) values of C and S are C = 23 and S = 21.
In other words, after Candice completes 23 laps, and Sabrina completes 21 laps, both runners will be together at the starting point.
Answer: B
Cheers,
Brent