MHB Problem using this formula both ways

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The discussion focuses on a method for calculating speed and distance using a specific formula. A car that traveled 27 miles in 120 minutes is calculated to have a speed of 13.5 mph by manipulating the numbers and converting units. The poster seeks similar calculations for different scenarios, such as determining distance traveled at 42 mph for 73 minutes and average speed for a 52-mile journey in 39 minutes. They argue that their method simplifies unit conversions and makes the calculations more intuitive. Overall, the approach emphasizes clarity in understanding speed and distance relationships.
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Okay, so I've messed about with this for a while now and I've found that the following formula works on how to get the speed.

A car has covered 27 miles in 120 minutes. What is the speed it is traveling at?

I add three zeros to the 27, making it 27,000.

120/27000 = 225. I then put a decimal point at the start of the three digit number (if it were a 4 digit number, for example; 2225, I'd make it 2.225) but for this particular sum the number is 0.225.

0.225 x 60 = 13.500mph

I have found this method works, and its very easy!Now, I'm trying to use a similar method to use in order to obtain distances and speed.
For example, could someone answer the following setting it out the same way I did with the mph formula?

A car has been traveling 42 mph for 73 minutes, how far (in miles) has it travelled?

A car has traveled 52 miles in 39 minutes, what is the car's average speed?
 
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Personally, I find it much easier to write:

$$\overline{v}=\frac{d}{t}=\frac{27\text{ mi}}{120\text{ min}}\cdot\frac{60\text{ min}}{1\text{ hr}}=\frac{27}{2}\text{ mph}=13.5\text{ mph}$$

To me it is much more obvious what is going on. For example, suppose we wish to convert a speed given in mph to m/s. We could simply write:

$$v\text{ mph}=v\frac{\text{mi}}{\text{hr}}\cdot\frac{127\text{ cm}}{50\text{ in}}\cdot\frac{12\text{ in}}{1\text{ ft}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ m}}{100\text{ cm}}\cdot\frac{1\text{ hr}}{3600\text{ s}}=\frac{1397}{3125}v\frac{\text{m}}{\text{s}}$$

I think you will find this method will serve you better in all types of unit conversions.
 
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