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Ken and Hamid run around a track. It takes Ken 80 seconds to complete a lap. It takes Hamid 60 seconds to complete a lap. Ken and Hamid start running at the same time from the start line. How many laps will they each have run when they next meet on the start line?
The correct answer is:
Ken will have run 3 laps and Hamid will have run 4.
Explanation:
To find this, we first find the number of seconds that will have passed when they meet again. We use the LCM, or least common multiple, for this. First we find the prime factorization of each number:
80 = 10(8)
10 = 5(2)
8 = 2(4)
4 = 2(2)
80 = 2(2)(2)(5)(2)
60 = 10(6)
10 = 5(2)
6 = 2(3)
60 = 2(2)(3)(5)
For the LCM, we multiply the common factors by the uncommon. Between the two numbers, the common factors are 2, 2 and 5. This makes the uncommon 2, 2, and 3, and makes our LCM
2(2)(5)(2)(2)(3) = 240
This means every 240 seconds they will both be at the start line.
Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.
Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.
Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] laps when they next meet on the start line.
Take LCM of [tex]80,60 =240\\[/tex]
After every [tex]240[/tex] seconds they will both be at the start line.
So in [tex]240[/tex] seconds Ken covered
[tex]\dfrac{240}{80}=3laps\\[/tex]
So in [tex]240[/tex] seconds Hamid covered
[tex]\dfrac{240}{60}=4laps\\[/tex]
Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] Laps.
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The expression 625(1−x) gives the discounted price of a television, where x is the percent of the discount written in decimal form. What does the 625 represent in the expression?
the original price of the television
the percent of the original price being paid the discounted price of
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Halle is hiking down into a canyon. She descends 3,000 ft in 1 3/4 hours. To the nearest foot, what number shows her descent per hour?
Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added two over three of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe, or did he go over and by what amount?
Jeff has added 53.33 grams more vanilla powder than the recipe.
The recipe calls for 32 grams of vanilla powder, and we need to compare this to the amount Jeff used.
Jeff added two-thirds of a cup of vanilla powder to the flour. Since 1 cup of vanilla powder is 128 grams, two-thirds of that amount can be calculated as follows:
(2/3) × 128 grams = 85.33 grams (rounded to two decimal places).
Comparing this to the requested 32 grams, Jeff has added more than the recipe asks for:
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If a revolving restaurant can rotate 270° in 45 minutes, how long does it take for the restaurant to make a complete revolution?
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Step-by-step explanation:
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Step-by-step explanation:
To write expressions equivalent to 20x + 100, we can use factoring, distributing, and properties of equality. Examples include 4(5x + 25), 10(2x + 10), and three other variations, all of which maintain the original value of the expression.
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