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Nataliya [291]
2 years ago
12

Two buses leave towns 304 miles apart at the same time and travel toward each other. One bus travels 14 mih slower than the othe

r. If they meet in 2 hours, what is the rate of each bus?
Mathematics
1 answer:
8090 [49]2 years ago
7 0

Answer:

The faster bus moves at 83mi/h and the slower one moves at 69mi/h.

Step-by-step explanation:

Let's define:

R₁ = rate of bus 1, this is the faster one.

R₂ = rate of bus 2, this is the slower one.

We know that one bus travels 14mi/h slower, then:

R₂ = R₁ - 14mi/h.

Now we know that:

Distance = Speed*Time.

If we add the distances that both busses travel in 2 hours, it should be equal to the initial distance between the buses, then:

R₁*2h + R₂*2h = 304 mi

Then we have the two equations:

R₂ = R₁ - 14mi/h

R₁*2h + R₂*2h = 304 mi

The first step is to replace the first equation in the second one, to get:

R₁*2h + (R₁ - 14mi/h)*2h = 304 mi

And now we can solve this for R₁.

R₁*2h + R₁*2h - 14mi/h*2h = 304 mi

R₁*4h - 28mi = 304mi

R₁*4h = 304mi + 28mi = 332mi

R₁ = 332mi/4h = 83mi/h

The faster bus moves at 83mi/h

And we know that the slower one moves at 14mi/h slower than this, then:

R₂ = R₁ - 14mi/h = 83mi/h - 14mi/h = 69 mi/h

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Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of
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Answer:

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Step-by-step explanation:

You must have heard about Arithmetic Progressions (AP)

Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

Our very own counting numbers form AP

For example :-

2 = 1 + <u>1</u>

3 = 2 + <u>1</u>

4 = 3 + <u>1</u>

The number in bold (1) is that constant number which is added to a number to form its successive number.

To find the sum of series forming AP, we use the formula :-

sum =  \frac{n}{2} \{ a  + a  _{n}  \}

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So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

and n is 25

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So, the value of S comes out to be 325.

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AE: AC = AD:AB

(ONCE YOU KNOW AB YOU CAN SUBTRACT AD FROM AB TO GET BD =20)

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