Question

Question #f5cc7

Answer 1

Its speed is 1206 mph.

Explanation:

This is an exercise in unit conversions.

In this question, we must somehow convert metres to miles and seconds to hours.

The conversions I remember are

• `"1 m = 39.37 in"`
• `"12 in = 1 ft"`
• `"5280 ft = 1 mi"`
• `"60 s = 1 min"`
• `"60 min = 1 h"`

Let's put these all together.

`(539.0 color(red)(cancel(color(black)("m"))))/(1 color(red)(cancel(color(black)("s")))) × (39.37 color(red)(cancel(color(black)("in"))))/(1 color(red)(cancel(color(black)("m")))) × (1 color(red)(cancel(color(black)("ft"))))/(12 color(red)(cancel(color(black)("in")))) × "1 mi"/(5280 color(red)(cancel(color(black)("ft")))) × (60 color(red)(cancel(color(black)("s"))))/(1 color(red)(cancel(color(black)("min")))) × (60 color(red)(cancel(color(black)("min"))))/"1 h" = "1206 mi/h"`

Answer 2

`"1206 mi/hr"`

Explanation:

I will use four conversion factors here, two to convert the distance from meters to miles and two to convert the time from seconds to hours.

More specifically, I will use

`"1 km" = 10^3"m" " "` and `" " "1 mi " = " 1.609344 km"`

`"1 min " = " 60 s" " "` and `" " "1 hr " = " 60 min"`

I'll add the conversion factors for distance first, then the conversion factors for time.

`539.0 * color(blue)(cancel(color(black)("m")))/(1color(red)(cancel(color(black)("s")))) * (1color(orange)(cancel(color(black)("km"))))/(10^3color(blue)(cancel(color(black)("m")))) * "1 mi"/(1.609344color(orange)(cancel(color(black)("km")))) * (60color(red)(cancel(color(black)("s"))))/(1color(purple)(cancel(color(black)("min")))) * (60color(purple)(cancel(color(black)("min"))))/"1 hr" = color(darkgreen)(ul(color(black)("1206 mi/hr")))`

The answer is rounded to four sig figs.

Notice that you can also use the four conversion factors to form a single conversion factor that takes you directly from meters per second to miles per hour

`(1color(blue)(cancel(color(black)("m"))))/(1color(red)(cancel(color(black)("s")))) * (1color(orange)(cancel(color(black)("km"))))/(10^3color(blue)(cancel(color(black)("m")))) * "1 mi"/(1.609344color(orange)(cancel(color(black)("km")))) * (60color(red)(cancel(color(black)("s"))))/(1color(purple)(cancel(color(black)("min")))) * (60color(purple)(cancel(color(black)("min"))))/"1 hr" = "2.2369 mi/hr"`

You will once again have

`539.0 color(red)(cancel(color(black)("m/s"))) * "2.2369 mi/hr"/(1color(red)(cancel(color(black)("m/s")))) = color(darkgreen)(ul(color(black)("1206 mi/hr")))`