You and a friend are running on treadmills. you run 0.5 mile every 3 minutes and your friend runs 2 miles every 14 minutes. you both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run?
2 answers:
I run 1 mile every 6 minutes. My friend runs 1 mile every 7 minutes. Lowest Common Multiple: LCM ( 6, 7 ) = 42 minutes. Me : 42 : 6 = 7 miles My friend : 42 : 7 = 6 miles .
Start by finding how long it takes each to run 1 mile. You: 0.5 mile every 3 minutes => 1 mile every 6 minutes Your friend 2 miles every 14 minutes => 1 mile every 7 minutes Now you have to calculate the minimum common multiple of 6 and 7. For that you need to factor both numbers and take common and non common factors raised to their highest exponent: 6 = 3*2 7 = 7 Then the minimum common multiple is 2*3*7=42. Now divide the time 42 by the humber of minutes each of you take to run 1 mile you: 42 minutes / 6 minutes per mile = 7 miles your friend 42 minutes / 7 minutes per mile = 6 miles. You can run 7 miles and your friend 6 miles in the same time. Answer: 7 and 6
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