Question

Convert units on the following time rates. 4.86 feet per second to miles per hour.

Short answer

4.86 feet per second is approximately 3.31 miles per hour.

Step-by-step solution

Convert feet to miles

Since there are 5280 feet in a mile, divide the number of feet by 5280 to convert to miles. Calculation: \(\frac{4.86 \text{ feet}}{5280}\)

Convert seconds to hours

As there are 3600 seconds in an hour (60 seconds in a minute and 60 minutes in an hour), multiply the number of seconds by 3600 to convert to hours.Calculation: \(4.86 \times 3600\)

Calculate miles per hour

Combine the conversions from feet to miles and seconds to hours to find the speed in miles per hour.Calculation: \(\frac{4.86}{5280} \times 3600 \text{ mph}\)

Perform the calculation

Complete the multiplication and division to get the final answer.Calculation: \(4.86 \times \frac{3600}{5280} = 3.31 \text{ mph}\)

Key concepts

Feet to Miles Conversion

When working with distances or lengths, it's sometimes necessary to convert units from feet to miles, especially in the United States where both units are commonly used. To convert feet to miles, one must remember the basic conversion factor: 1 mile is equal to 5280 feet.

So, the formula to convert feet to miles is simply: \[ \text{miles} = \frac{\text{feet}}{5280} \].

This conversion step is important for various applications such as mapping distances, calculating speed for travel, or even preparing for a race. In the example provided, one would take the 4.86 feet per second and divide it by 5280 to obtain the distance in miles. This serves as the first step in a larger calculation, such as finding out how fast something is moving.

Time Rate Conversion

Understanding time rate conversion is crucial for problems involving speed or rate of change. Generally, we might encounter rates given in different time units - like seconds, minutes, or hours - and converting correctly between these units is essential.

To convert from smaller time units to larger ones (for example, seconds to hours), one should know that there are 60 seconds in a minute and 60 minutes in an hour, totaling 3600 seconds in an hour. Thus, when you have a rate in seconds and you want to find out the equivalent rate in hours, multiply by 3600.\[ \text{hours} = \text{seconds} \times \frac{1}{3600} \].

For instance, in the exercise example, to convert a rate from feet per second to miles per hour, you first address the 'per second' part by multiplying the initial value by 3600, thereby scaling the rate from a second to an hourly basis.

Calculating Speed

The concept of calculating speed is a practical application of unit conversions in the context of rate. Speed signifies how fast an object travels over a certain distance within a given time frame. It is often expressed in terms like 'miles per hour' (mph) or 'kilometers per hour' (kph).

To calculate speed in a specific unit, one must ensure that the distance and time units are compatible. In the example exercise, after converting feet to miles and seconds to hours, we combine these to get the speed in miles per hour by the formula:\[ \text{speed (mph)} = \frac{\text{distance (miles)}}{\text{time (hours)}} \].

Thus, taking our converted distance and time from the earlier conversion steps, we now have the appropriate units to multiply and find the speed. This final step combines our understanding of unit conversion with the formula for speed to arrive at the desired outcome. After the relevant calculations, we establish that an object traveling at 4.86 feet per second is moving at a speed of approximately 3.31 miles per hour.