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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?

Explanation	Calculations	Help
$We first factor each rider's lap time into prime numbers.$	$42 = 2 \times 3 \times 7 46 = 2 \times 23$
$We now find the least common multiple of the two lap times by taking each prime with its highest needed exponent.$	$LCM = 2 \times 3 \times 7 \times 23 = 966$	Theory & Tactics Method Card DIV6-A Click to view full details
$Candice's number of laps equals the total time until they meet divided by her lap time, so we write this division in factored form before simplifying.$	$\frac{966}{42} = \frac{2 \times 3 \times 7 \times 23}{2 \times 3 \times 7}$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We cancel out the common factors to obtain Candice's lap count.$	$\frac{2 \times 3 \times 7 \times 23}{2 \times 3 \times 7} = \frac{2 \times 3 \times 7 \times 23}{2 \times 3 \times 7} = 23$	Theory & Tactics Method Card FDPR2-A Click to view full details

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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?

Explanation	Calculations	Help
$We first factor each rider's lap time into prime numbers.$	$42 = 2 \times 3 \times 7 46 = 2 \times 23$
$We now find the least common multiple of the two lap times by taking each prime with its highest needed exponent.$	$LCM = 2 \times 3 \times 7 \times 23 = 966$	Theory & Tactics Method Card DIV6-A Click to view full details
$Candice's number of laps equals the total time until they meet divided by her lap time, so we write this division in factored form before simplifying.$	$\frac{966}{42} = \frac{2 \times 3 \times 7 \times 23}{2 \times 3 \times 7}$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We cancel out the common factors to obtain Candice's lap count.$	$\frac{2 \times 3 \times 7 \times 23}{2 \times 3 \times 7} = \frac{2 \times 3 \times 7 \times 23}{2 \times 3 \times 7} = 23$	Theory & Tactics Method Card FDPR2-A Click to view full details

Scroll horizontally to view all columns

23