Systems and rate problems

TL;DR

Jason traveled 25 miles by train and 5 miles by bike in a total of 1 hour.

Transcript

Jason bicycled from home to the train station at an average speed of 10 miles per hour. Then he boarded a train and traveled into the city at an average speed of 50 miles per hour. The entire distance was 30 miles; the entire trip took 1 hour. How many miles did Jason travel by train? So let's write that down as a variable. So let's say distance, a... Read More

Key Insights

• 🚄 Jason traveled at different speeds during his bike and train rides.
• 😀 The total distance covered by Jason was 30 miles.
• 😀 By setting up equations based on the given information, the distance traveled by train was found to be 25 miles.

Questions & Answers

Q: What was Jason's average speed during his bike ride?

Jason's average speed during his bike ride was 10 miles per hour since he traveled a distance of 5 miles in an hour.

Q: What was Jason's average speed during the train ride?

Jason's average speed during the train ride was 50 miles per hour since he traveled a distance of 25 miles in an hour.

Q: How did the given information help in finding the distance traveled by train?

The given information allowed us to set up two equations and two unknowns which we could solve simultaneously to find the distance traveled by train.

Q: How was the equation for time derived?

The equation for time was derived using the formula distance = rate * time, where rate is the speed and time is the time taken to travel a certain distance.

Summary & Key Takeaways

• Jason traveled from home to the train station at an average speed of 10 miles per hour.

• He then boarded a train and traveled into the city at an average speed of 50 miles per hour.

• The entire trip covered a distance of 30 miles and took 1 hour.