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Neporo4naja [7]
3 years ago
10

Two people start jogging at the same point and time but in opposite directions. If the rate of one jogger is 2 mph faster than t

he other and after 3 hours they are 30 miles apart, what is the rate of the faster jogger
A 3
B 4
C 5
D 6
E 7
Mathematics
1 answer:
Zielflug [23.3K]3 years ago
6 0

Answer:

D: 6

Step-by-step explanation:

Let x mph be the rate of the faster jogger

Therefore (x-2) mph is the rate of the slower jogger

After 3 hours faster jogger will be 3x miles from the starting point

Whereas after the 3 hours slower jogger will be 3(x-2) miles from the starting point but in the opposite direction.

Since they are 30 miles apart 3x+3(x-2)=30

3x+3x-6=30

⇒ 3x+3x=30 +6

⇒ 6x=36

⇒ x=6

Therefore the rate of the faster jogger = 6 mph

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Maru [420]

9514 1404 393

Answer:

  D.

Step-by-step explanation:

The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)

When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.

The only reasonable choice is D.

__

Your calculator can check this for you.

  √12/(√3 +3) ≈ 3.4641/(1.7321 +3)

  = 3.4641/4.7321 ≈ 0.7321 = -1 +√3

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If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.

  \displaystyle\frac{\sqrt{12}}{\sqrt{3}+3}=\frac{\sqrt{12}}{(\sqrt{3}+3)}\cdot\frac{(\sqrt{3}-3)}{(\sqrt{3}-3)}=\frac{\sqrt{36}-3\sqrt{12}}{3-9}\\\\=\frac{6-3\cdot2\sqrt{3}}{-6}=\boxed{-1+\sqrt{3}}

_____

<em>Additional comment</em>

We "rationalize the denominator" in this way to take advantage of the relation ...

  (a -b)(a +b) = a² -b²

Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.

We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).

3 0
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The appropriate choice is ...

... c. -8

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