The time it takes John to get to the store is inversely proportional to his rate. John walks at a rate of 3 miles per hour. It takes him 20 minutes to walk to the store. He rides his bike at a rate of 15 miles per hour. How long would it take John to ride his bike to the store?
4 min
100 min
8 min
2.25 min
We can set up an inverse proportion equation to solve for the time it would take John to ride his bike to the store:
rate * time = constant
For walking, we have:
3 mph * 20 min = constant
To find the constant, we convert the time to hours:
20 min = 20/60 hours = 1/3 hours
Now we can solve for the constant:
3 mph * 1/3 hours = constant
1 mph = constant
Now we can use the constant to find the time it would take John to ride his bike:
15 mph * time = 1 mph
Simplifying the equation:
time = 1/15 hours
Converting the time to minutes:
1/15 hours * 60 min/hour = 4 min
Therefore, it would take John 4 minutes to ride his bike to the store.
To solve this problem, we can use the concept of inverse proportionality between time and rate.
Let's denote the time it takes for John to ride his bike to the store as "x" (in minutes).
According to the given information, John's rate while riding his bike is 15 miles per hour.
Since we want to find the time in minutes, we can convert the rate to miles per minute by dividing it by 60 (since there are 60 minutes in an hour):
Rate (in miles per minute) = 15 miles per hour / 60 minutes per hour = 0.25 miles per minute.
Now we can set up the inverse proportion:
Time (in minutes) ∝ 1 / Rate (in miles per minute)
To write the proportion, we can set up the following equation:
20 minutes ∝ 1 / 3 miles per hour.
To solve for x, we can use the proportion:
20 minutes = k / 0.25 miles per minute, where k is the proportionality constant.
To find the value of k, we can cross-multiply:
20 minutes * 0.25 miles per minute = k
5 miles * minutes = k
Now we can substitute the value of k back into the equation to find x:
x = k / 0.25 miles per minute
x = 5 miles * minutes / 0.25 miles per minute
x = 20 minutes
Therefore, it would take John 20 minutes to ride his bike to the store.
So the correct answer is 20 minutes.
To determine the time it would take John to ride his bike to the store, we need to apply the concept of inverse proportionality.
The first step is to establish the inverse proportionality relationship between time and rate. In this case, the time it takes to get to the store is inversely proportional to the rate at which John is traveling.
Let's denote the time it takes to get to the store as T and the rate as R. The relationship can be expressed as T ∝ 1/R.
Since we know the rate of walking is 3 miles per hour, and it takes John 20 minutes to walk to the store, we can set up the following equation:
20 minutes = T * (1/3) hours
First, we need to convert the 20 minutes into hours. There are 60 minutes in an hour, so:
20 minutes = 20/60 = 1/3 hours
Now, we can plug in the values into our equation and solve for T:
1/3 = T * (1/3)
To isolate T, we multiply both sides by 3:
1 = T
Therefore, it would take John 1 hour to walk to the store.
Next, let's determine the time it would take John to ride his bike to the store. We know that the rate of riding his bike is 15 miles per hour. Let's set up a similar equation:
T = R * (1/15)
Substituting the rate of 15 miles per hour:
T = 1/15
To convert the time T into minutes, we multiply it by 60:
T = (1/15) * 60 = 4 minutes
Thus, it would take John 4 minutes to ride his bike to the store.
Therefore, the correct answer is 4 minutes.