Multiple rates word problem | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy

TL;DR

Umaima traveled to a gift store uphill for 45 minutes at a speed of 8 miles per hour and then traveled back downhill at a speed of 24 miles per hour. Her average speed for the entire trip is 12 miles per hour.

Transcript

Starting at home, Umaima traveled uphill to the gift store for 45 minutes at just 8 miles per hour. She then traveled back home along the same path downhill at a speed of 24 miles per hour. What is her average speed for the entire trip from home to the gift store and back? So we're trying to figure out her average speed for the entire trip. That's ... Read More

Key Insights

• 🐎 Average speed is calculated by dividing the total distance traveled by the total time taken.
• 🛝 To find the total distance for a round trip, double the distance to the destination.
• ⌛ The total time for a round trip is the sum of the time to the destination and the time to return.
• 🐎 The distance to the destination can be found by multiplying the time taken by the speed.

Questions & Answers

Q: How can we calculate Umaima's average speed for the entire trip?

To calculate the average speed, we need to find the total distance and the total time. The total distance is 2 times the distance to the gift store, which is 12 miles. The total time is the sum of the time to the gift store (45 minutes or 3/4 hours) and the time to come back (1/4 hour). Therefore, her average speed is 12 miles divided by 1 hour, which is 12 miles per hour.

Q: Why do we double the distance to the gift store to find the total distance?

The distance to the gift store and the distance back from the gift store is the same, so we can consider it as a round trip. Therefore, the total distance is 2 times the distance to the gift store.

Q: How do we calculate the distance to the gift store?

We are given the time it takes Umaima to travel to the gift store (45 minutes or 3/4 hours) and her speed (8 miles per hour). By multiplying the time by the speed, we can find the distance to the gift store, which is 6 miles.

Q: Why is Umaima's average speed not the average of her speeds uphill and downhill?

Umaima traveled at different speeds for different amounts of time. To calculate the average speed, we need to consider the total distance and total time. Simply averaging her speeds would not give an accurate representation of her average speed for the entire trip.

Summary & Key Takeaways

• Umaima traveled uphill to a gift store for 45 minutes at a speed of 8 miles per hour.

• She then traveled back downhill to her home along the same path at a speed of 24 miles per hour.

• The average speed for her entire trip from home to the gift store and back is 12 miles per hour.