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

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BTGmoderatorLU: Moderator; Posts: 2554; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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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Source: Beat The GMAT — Problem Solving | Fri Aug 02, 2024 1:46 pm

malarkey: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Aug 07, 2024 8:06 am

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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