Question

Question #e6d37

Answer 1

`"57.2 ft/s"`

Explanation:

In order to solve this, we will use dimensional analysis.

First, to eliminate the `"mi"` unit, multiply by `"5280 ft" / "1 mi"`. Since `"1 mi = 5280 ft"`, you are essentially multiplying by `1`.

`("156" cancel("mi")) / "4 hr" * color(blue)("5280 ft" / ("1" cancel("mi")))`

Now, we are left with `"ft"/"hr"`. We want the final unit to be `"ft"/"s"`, so we can use the conversion factors `"1 hr = 60 min"` and `"1 min = 60 s"`.

`("156" cancel("mi")) / ("4" cancel("hr")) * "5280 ft" / ("1" cancel("mi")) * color(blue)(("1" cancel("hr")) / "60 min")` `->` cancels out the `"hr"` unit

`("156" cancel("mi")) / ("4" cancel("hr")) * "5280 ft" / ("1" cancel("mi")) * ("1" cancel("hr")) / ("60" cancel("min")) * color(blue)(("1" cancel("min"))/ "60 s")` `->` cancels out the `"min"` unit

Now, we are left with our desired unit of `"ft"/"s"`. Finally, multiply and divide the remaining numbers.

`(156 * "5280 ft") / (4 * 60 * "60 s") = "57.2 ft/s"`

So, `"156 mi" / "4 hr"` `=` `"57.2 ft/s"`.

Answer 2

`57.2` feet per second

Explanation:

By 'unit rate', we mean how many of the first quantity for ONE of the second unit.

So, by 'feet per second, we mean, how many feet are covered in ONE second?

We can convert the given quantities to the required units:

`156 " miles: " 156 xx 1760 xx 3 = 823,680 " feet"`

miles `rarr` yards `rarr` feet

`4 " hours: " 4 xx 60 xx 60 =14,400 " seconds"`

hours `rarr` minutes `rarr` seconds

`(823,680" feet ")/(14,400" seconds ") =57.2` feet per second.