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You and your friend stand back to back and then sprint in exactly opposite
directions at constant rates. After 10 seconds, you have gone 19 meters, and your
friend has gone 27 meters. From your perspective, how fast was your friend
moving away from you?



Answer :

GinnyAnswer
Sure, let's break down the problem step by step:

1. Calculate Your Speed:
- You have traveled 19 meters in 10 seconds.
- Speed is calculated as the distance traveled divided by the time taken.
- Therefore, your speed is: [tex]\[ \text{Your speed} = \frac{\text{Distance}}{\text{Time}} = \frac{19 \text{ meters}}{10 \text{ seconds}} = 1.9 \text{ meters/second} \][/tex]

2. Calculate Your Friend's Speed:
- Your friend has traveled 27 meters in 10 seconds.
- Similarly, their speed is: [tex]\[ \text{Friend's speed} = \frac{\text{Distance}}{\text{Time}} = \frac{27 \text{ meters}}{10 \text{ seconds}} = 2.7 \text{ meters/second} \][/tex]

3. Determine the Relative Speed:
- Since you and your friend are moving in opposite directions, the relative speed between you two is the sum of your individual speeds.
- Therefore, the relative speed is: [tex]\[ \text{Relative speed} = \text{Your speed} + \text{Friend's speed} = 1.9 \text{ meters/second} + 2.7 \text{ meters/second} = 4.6 \text{ meters/second} \][/tex]

Thus, from your perspective, your friend was moving away from you at a speed of 4.6 meters per second.

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