An elephant and a lion are currently $1$ mile apart. The elephant runs directly away from the lion at $19$ miles per hour, while the lion runs directly towards the elephant at $24$ miles per hour. How many minutes will it take for the lion to catch the elephant?

To determine the time it takes for the lion to catch the elephant, we need to calculate the relative speed at which the lion is closing the distance between them.

The elephant runs away from the lion at a speed of $19$ miles per hour, while the lion runs towards the elephant at a speed of $24$ miles per hour.

The relative speed at which the lion is catching up to the elephant is:
\[
24 \text{ miles per hour} - 19 \text{ miles per hour} = 5 \text{ miles per hour}
\]

Next, we need to find the time it takes for the lion to cover the initial distance of $1$ mile at this relative speed of $5$ miles per hour.

The formula to calculate time when distance and speed are known is:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

Using this formula, the time $ t $ in hours is:
\[
t = \frac{1 \text{ mile}}{5 \text{ miles per hour}} = 0.2 \text{ hours}
\]

To convert this time into minutes, we use the fact that $1$ hour equals $60$ minutes:
\[
0.2 \text{ hours} \times 60 \text{ minutes per hour} = 12 \text{ minutes}
\]

Therefore, it will take the lion $12$ minutes to catch the elephant.

Do you want details or have any questions?

Here are 5 more questions you might find interesting:
1. How long will it take for a car traveling at 60 mph to cover 150 miles?
2. What is the relative speed of two trains traveling towards each other, one at 80 mph and the other at 70 mph?
3. If a runner increases their speed from 6 mph to 8 mph, how much time do they save over a 5-mile distance?
4. How long will it take to fill a 1000-liter tank with a pump that flows at a rate of 50 liters per minute?
5. What is the stopping distance for a car traveling at 60 mph if the braking distance is proportional to the square of the speed?

Tip: Always double-check the units in your calculations to ensure accuracy.

Learn how to calculate the time it takes for a lion running towards an elephant to catch up, given their speeds and starting distance. This problem involves understanding relative speed and applying the time-speed-distance formula. Suitable for Grades 7-9.

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