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Yesterday, Ethan and Maria practiced sprinting around an oval track. They both started at the same time from the starting line. Ethan completes each lap in 38 seconds, while Maria completes each lap in 50 seconds. How many laps around the track has Ethan completed the next time that they are together at the starting point?

Explanation	Calculations	Help
$We first factor each sprinter's lap time into prime numbers.$	$38 = 2 \times 19 50 = 2 \times 5 \times 5$
$We now find the least common multiple of the two lap times by taking each prime with its highest exponent.$	$LCM = 2 \times 19 \times 5 \times 5 = 950$	Theory & Tactics Method Card DIV6-A Click to view full details
$Ethan's number of laps equals the total time until they meet divided by his lap time.$	$\frac{950}{38} = \frac{2 \times 5 \times 5 \times 19}{2 \times 19}$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We cancel out the common factors to obtain Ethan's lap count.$	$\frac{2 \times 5 \times 5 \times 19}{2 \times 19} = \frac{2 \times 5 \times 5 \times 19}{2 \times 19} = 25$	Theory & Tactics Method Card FDPR2-A Click to view full details

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B

Yesterday, Ethan and Maria practiced sprinting around an oval track. They both started at the same time from the starting line. Ethan completes each lap in 38 seconds, while Maria completes each lap in 50 seconds. How many laps around the track has Ethan completed the next time that they are together at the starting point?

Explanation	Calculations	Help
$We first factor each sprinter's lap time into prime numbers.$	$38 = 2 \times 19 50 = 2 \times 5 \times 5$
$We now find the least common multiple of the two lap times by taking each prime with its highest exponent.$	$LCM = 2 \times 19 \times 5 \times 5 = 950$	Theory & Tactics Method Card DIV6-A Click to view full details
$Ethan's number of laps equals the total time until they meet divided by his lap time.$	$\frac{950}{38} = \frac{2 \times 5 \times 5 \times 19}{2 \times 19}$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We cancel out the common factors to obtain Ethan's lap count.$	$\frac{2 \times 5 \times 5 \times 19}{2 \times 19} = \frac{2 \times 5 \times 5 \times 19}{2 \times 19} = 25$	Theory & Tactics Method Card FDPR2-A Click to view full details

Scroll horizontally to view all columns

B