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A train traveled for three hours. In the first hour the train traveled \(86\) miles, which was \(25\%\) farther than

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A train traveled for three hours. In the first hour the train traveled \(86\) miles, which was \(25\%\) farther than

by BTGmoderatorLU » Fri Aug 02, 2024 1:46 pm

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A train traveled for three hours. In the first hour the train traveled \(86\) miles, which was \(25\%\) farther than it traveled in the second hour. In the third hour the train traveled at a speed of \(120\) miles per hour for \(20\) minutes. What is the total distance that the train traveled?

A. \(190.6\)
B. \(194.8\)
C. \(198.2\)
D. \(204.5\)
E. \(212.8\)

The OA is B
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Re: A train traveled for three hours. In the first hour the train traveled \(86\) miles, which was \(25\%\) farther than

by malarkey » Wed Aug 07, 2024 8:21 am
To determine the total distance traveled by the train, we need to break down the problem hour by hour.

1. First Hour:
- The train traveled 86 miles in the first hour.

2. Second Hour:
- We know that 86 miles was 25% farther than the distance traveled in the second hour.
- Let \( d \) be the distance traveled in the second hour.
- Thus, 86 miles = \( d + 0.25d \).
- Therefore, \( 86 = 1.25d \).
- Solving for \( d \):
\[
d = \frac{86}{1.25} = 68.8 \text{ miles}
\]

3. Third Hour:
- The train traveled at a speed of 120 miles per hour for 20 minutes.
- 20 minutes is \(\frac{20}{60} = \frac{1}{3}\) of an hour.
- Therefore, the distance traveled in the third hour is:
\[
\text{Distance} = 120 \text{ miles per hour} \times \frac{1}{3} \text{ hour} = 40 \text{ miles}
\]

4. Total Distance Traveled:
- Add the distances from each hour:
\[
\text{Total distance} = 86 \text{ miles} + 68.8 \text{ miles} + 40 \text{ miles}
\]
\[
\text{Total distance} = 194.8 \text{ miles}
\]

Thus, the total distance that the train traveled is \( \boxed{194.8} \).
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