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Helga [31]
3 years ago
6

6. Two joggers start at the same time from opposite ends of a 10 km course. One jogger is running at 6 km/hr and the other is ru

nning at 10 km/hr. How long after they start will they meet?​
Mathematics
1 answer:
Luda [366]3 years ago
5 0

Answer:

In this problem, we are basically finding the LCM of the two numbers.

LCM means the smallest common multiple of two or more numbers.

For example, the LCM of 5 and 10 would be 10, because 5 can go into 10.

Another example would be the LCM of 9 and 6. The answer would be 18, because both numbers can go into 18 and that is the smallest it can go.

Step-by-step explanation:

So, in this problem, we are finding the LCM of 10 and 6.

The LCM of 10 and 6 would be 30.

If you thought it was 60, you are correct, but the two numbers have a smaller similarity.

10: 10, 20, 30, 40, 50, 60.

6: 6, 12, 18, 24, 36, 42, 48, 54, and 60.

As you can see, 30 is the best choice to pick.

Hope this helps and have an amazing day!

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a) The solution for the equation 2x + 16 = 5x + 4  is x=4.

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c) The solution for the equation 5x − 5 = x + 15 is x=5.

<u>Step-by-step explanation:</u>

<u>a) The given equation is  2x + 16 = 5x + 4 </u>

  • From the above equation, it can be found that the equation consists of x terms and constant terms.
  • Therefore, bring all the x terms on one side and the constant terms on other side of the equation.
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⇒ 16-4 = 5x-2x

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The solution for the given equation is x=4.

<u>To check, substitute x=4 in the equation :</u>

2(4) + 16 = 5(4) + 4

8+16 = 20+4

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<u>b) The given equation is 3x − 5 = 2x + 14</u>

⇒ 3x-2x = 14+5

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The solution for the given equation is x=19.

<u>To check, substitute x=19 in the equation :</u>

3(19) - 5 = 2(19) + 14

57-16 = 38+14

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Therefore, the solution x=19 satisfies the equation 3x − 5 = 2x + 14

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<u>c) The given equation is 5x − 5 = x + 15</u>

⇒ 5x-x = 15+5

⇒ 4x = 20

⇒ x = 20/4

⇒ x = 5

The solution for the given equation is x=5.

<u>To check, substitute x=5 in the equation :</u>

5(5) - 5 = 5 + 15

25-5 = 20

20 = 20

Therefore, the solution x=5 satisfies the equation 5x − 5 = x + 15

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