Question
gertrude and russel are tevling on their motor scoopers in the same direction along the same road. gertrude is traving at 10 mph and is exactly 3 miles ahead of russel, whos is traveling at 14mph. How many hours will it take russel to catch gertrude?(write your answer as a decimal)
Answers
GPT-4o
To determine how long it will take for Russel to catch up to Gertrude, we need to figure out the time it takes for the distance between them, which starts at 3 miles, to close to 0.
1. **Speed of Gertrude:** 10 mph
2. **Speed of Russel:** 14 mph
3. **Initial distance between them:** 3 miles
The relative speed at which Russel is gaining on Gertrude is the difference between their speeds:
\[
14 \, \text{mph} - 10 \, \text{mph} = 4 \, \text{mph}
\]
Next, we need to determine the time \( t \) it takes for Russel to close this 3-mile gap at a relative speed of 4 mph:
\[
\text{Time (hrs)} = \frac{\text{Distance (miles)}}{\text{Relative Speed (mph)}} = \frac{3 \, \text{miles}}{4 \, \text{mph}} = 0.75 \, \text{hours}
\]
Therefore, it will take Russel 0.75 hours to catch up to Gertrude.
1. **Speed of Gertrude:** 10 mph
2. **Speed of Russel:** 14 mph
3. **Initial distance between them:** 3 miles
The relative speed at which Russel is gaining on Gertrude is the difference between their speeds:
\[
14 \, \text{mph} - 10 \, \text{mph} = 4 \, \text{mph}
\]
Next, we need to determine the time \( t \) it takes for Russel to close this 3-mile gap at a relative speed of 4 mph:
\[
\text{Time (hrs)} = \frac{\text{Distance (miles)}}{\text{Relative Speed (mph)}} = \frac{3 \, \text{miles}}{4 \, \text{mph}} = 0.75 \, \text{hours}
\]
Therefore, it will take Russel 0.75 hours to catch up to Gertrude.