Math / Algebra

QuestionWarren runs races to support local charities. In April, he ran a 5-kilometer race in 30 minutes to support his local hospital. In October, he will run a 10-kilometer race to support the animal shelter. If he runs at the same rate, how many minutes will it take Warren to run the race in October?

Studdy Solution

STEP 1

What is this asking? If Warren runs twice the distance at the same speed, how much longer will it take? Watch out! Don't forget that the distances are different!
We need to figure out how much longer the second race is compared to the first race.

STEP 2

1. Calculate Warren's speed
2. Calculate the time for the October race

STEP 3

Alright, let's start by figuring out how fast Warren runs.
Speed is just distance divided by time.
We know Warren ran $5$ kilometers in $30$ minutes.

STEP 4

So, his speed is $5 \text{ km} / 30 \text{ min}$ .
Let's simplify that fraction by dividing both the top and bottom by $5$ .
This gives us $1 \text{ km} / 6 \text{ min}$ .
That means Warren runs one kilometer every six minutes!

STEP 5

Now, we know the October race is $10$ kilometers.
Since we know Warren's speed, we can figure out how long it will take him.

STEP 6

We can set up a simple equation: $\text{time} = \text{distance} / \text{speed}$ .
We plug in our values: $\text{time} = 10 \text{ km} / (1 \text{ km} / 6 \text{ min})$ .

STEP 7

Dividing by a fraction is the same as multiplying by its reciprocal, so we flip the fraction and multiply: $\text{time} = 10 \text{ km} \cdot (6 \text{ min} / 1 \text{ km})$ .

STEP 8

Notice how the "km" units cancel out by dividing to one, leaving us with: $\text{time} = 10 \cdot 6 \text{ min}$ .

STEP 9

Multiplying $10$ and $6$ gives us $60$ .
So, the time is $60$ minutes!

STEP 10

It will take Warren 60 minutes to run the 10-kilometer race in October.

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Studdy Solution

STEP 1

What is this asking? If Warren runs twice the distance at the same speed, how much longer will it take? Watch out! Don't forget that the distances are different!
We need to figure out how much longer the second race is compared to the first race.

STEP 2

1. Calculate Warren's speed
2. Calculate the time for the October race

STEP 3

Alright, let's start by figuring out how fast Warren runs.
Speed is just distance divided by time.
We know Warren ran $5$ kilometers in $30$ minutes.

STEP 4

So, his speed is $5 \text{ km} / 30 \text{ min}$ .
Let's simplify that fraction by dividing both the top and bottom by $5$ .
This gives us $1 \text{ km} / 6 \text{ min}$ .
That means Warren runs one kilometer every six minutes!

STEP 5

Now, we know the October race is $10$ kilometers.
Since we know Warren's speed, we can figure out how long it will take him.

STEP 6

We can set up a simple equation: $\text{time} = \text{distance} / \text{speed}$ .
We plug in our values: $\text{time} = 10 \text{ km} / (1 \text{ km} / 6 \text{ min})$ .

STEP 7

Dividing by a fraction is the same as multiplying by its reciprocal, so we flip the fraction and multiply: $\text{time} = 10 \text{ km} \cdot (6 \text{ min} / 1 \text{ km})$ .

STEP 8

Notice how the "km" units cancel out by dividing to one, leaving us with: $\text{time} = 10 \cdot 6 \text{ min}$ .

STEP 9

Multiplying $10$ and $6$ gives us $60$ .
So, the time is $60$ minutes!

STEP 10

It will take Warren 60 minutes to run the 10-kilometer race in October.

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Studdy Solution

STEP 1

What is this asking? If Warren runs twice the distance at the same speed, how much longer will it take? Watch out! Don't forget that the distances are different!We need to figure out how much longer the second race is compared to the first race.

STEP 2

1. Calculate Warren's speed2. Calculate the time for the October race

STEP 3

Alright, let's **start** by figuring out how fast Warren runs.Speed is just distance divided by time.We know Warren ran 555 kilometers in 303030 minutes.

STEP 4

So, his speed is 5 km/30 min5 \text{ km} / 30 \text{ min}5 km/30 min.Let's simplify that fraction by dividing both the **top** and **bottom** by 555.This gives us 1 km/6 min1 \text{ km} / 6 \text{ min}1 km/6 min.That means Warren runs **one kilometer every six minutes**!

STEP 5

Now, we know the October race is 101010 kilometers.Since we know Warren's speed, we can figure out how long it will take him.

STEP 6

We can set up a simple equation: time=distance/speed\text{time} = \text{distance} / \text{speed}time=distance/speed.We **plug in** our values: time=10 km/(1 km/6 min)\text{time} = 10 \text{ km} / (1 \text{ km} / 6 \text{ min})time=10 km/(1 km/6 min).

STEP 7

Dividing by a fraction is the same as multiplying by its reciprocal, so we flip the fraction and multiply: time=10 km⋅(6 min/1 km)\text{time} = 10 \text{ km} \cdot (6 \text{ min} / 1 \text{ km})time=10 km⋅(6 min/1 km).

STEP 8

Notice how the "km" units **cancel out** by dividing to one, leaving us with: time=10⋅6 min\text{time} = 10 \cdot 6 \text{ min}time=10⋅6 min.

STEP 9

Multiplying 101010 and 666 gives us 606060.So, the **time** is 606060 minutes!

STEP 10

It will take Warren **60 minutes** to run the 10-kilometer race in October.

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Start learning now

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What is this asking? If Warren runs twice the distance at the same speed, how much longer will it take? Watch out! Don't forget that the distances are different!
We need to figure out how much longer the second race is compared to the first race.

1. Calculate Warren's speed
2. Calculate the time for the October race

Alright, let's start by figuring out how fast Warren runs.
Speed is just distance divided by time.
We know Warren ran $5$ kilometers in $30$ minutes.

So, his speed is $5 \text{ km} / 30 \text{ min}$ .
Let's simplify that fraction by dividing both the top and bottom by $5$ .
This gives us $1 \text{ km} / 6 \text{ min}$ .
That means Warren runs one kilometer every six minutes!

Now, we know the October race is $10$ kilometers.
Since we know Warren's speed, we can figure out how long it will take him.

We can set up a simple equation: $\text{time} = \text{distance} / \text{speed}$ .
We plug in our values: $\text{time} = 10 \text{ km} / (1 \text{ km} / 6 \text{ min})$ .

Dividing by a fraction is the same as multiplying by its reciprocal, so we flip the fraction and multiply: $\text{time} = 10 \text{ km} \cdot (6 \text{ min} / 1 \text{ km})$ .

Notice how the "km" units cancel out by dividing to one, leaving us with: $\text{time} = 10 \cdot 6 \text{ min}$ .

Multiplying $10$ and $6$ gives us $60$ .
So, the time is $60$ minutes!

It will take Warren 60 minutes to run the 10-kilometer race in October.