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Erik biked north at a constant velocity for a total of 9 minutes. In one-third of that time, he moved 990 meters. What was Erik's velocity? Write your answer as a whole number. meters per minute to the north

Ask by Ortiz Alexander. in the United States
Feb 27,2025

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Answer

Erik's velocity was 330 meters per minute to the north.

Solution

To find Erik's velocity, we can follow these steps: 1. **Determine the total time of travel**: Erik biked for a total of 9 minutes. 2. **Calculate the time for one-third of the total time**: \[ \text{Time for one-third} = \frac{9 \text{ minutes}}{3} = 3 \text{ minutes} \] 3. **Distance traveled in one-third of the time**: Erik moved 990 meters in that time. 4. **Calculate the velocity**: Velocity is defined as distance divided by time. We can use the formula: \[ v = \frac{d}{t} \] where \( v \) is the velocity, \( d \) is the distance, and \( t \) is the time. Here, \( d = 990 \) meters and \( t = 3 \) minutes. 5. **Substituting the values**: \[ v = \frac{990 \text{ meters}}{3 \text{ minutes}} = 330 \text{ meters per minute} \] Thus, Erik's velocity is \( 330 \) meters per minute to the north.

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To find Erik's velocity, we first calculate the time he traveled. He biked for 9 minutes in total, and in one-third of that time, he traveled 990 meters. One-third of 9 minutes is 3 minutes. Now, velocity is defined as the total distance traveled divided by the total time taken. So, if Erik moved 990 meters in 3 minutes, we can determine his velocity by finding out how much he would travel in 9 minutes at the same speed. If he moved 990 meters in 3 minutes, we can scale that up to find how far he would go in 9 minutes: \[ \text{Distance in 9 minutes} = \text{Distance in 3 minutes} \times 3 = 990 \times 3 = 2970 \text{ meters} \] Now, we can calculate the velocity: \[ \text{Velocity} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2970 \text{ meters}}{9 \text{ minutes}} = 330 \text{ meters per minute} \] So, Erik's velocity was **330 meters per minute to the north**.

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