Convert 55mph to Millifurlongs per Microfortnight

[shortman12012]

Homework Statement

The speed limit on a particular stretch of road is 55 miles per hour. Express this speed limit in millifurlongs per microfortnight. A furlong is 1/8 mile, and a fortnight is a period of 2 weeks.

Homework Equations

The Attempt at a Solution

so what I tried doing was taking

55 mph ( 8furlong/1mile ) ( 336hours/1fortnight ) = 147840

8 furlongs are in one mile and 336hours are in 1 fortnight. However the answer that I got isn't correct so I need to know what I'm doing wrong please.

 

[Mark44]

Homework Statement

The speed limit on a particular stretch of road is 55 miles per hour. Express this speed limit in millifurlongs per microfortnight. A furlong is 1/8 mile, and a fortnight is a period of 2 weeks.

Homework Equations

The Attempt at a Solution

so what I tried doing was taking

55 mph ( 8furlong/1mile ) ( 336hours/1fortnight ) = 147840

8 furlongs are in one mile and 336hours are in 1 fortnight. However the answer that I got isn't correct so I need to know what I'm doing wrong please.

What you need to do is change mi/hr units to millifurlong/microfortnight units. It's helpful to write the units involved as fractions, because you want the units you don't want to cancel, so that you end up with the units you do want. For that reason I wrote mph as mi/hr.

Each of the expressions you have above in parentheses is a unit, hence is equal to 1. You can multiply by units all you want without changing the basic value of what you start with.

55 (mi/hr) * 8 (furlong/mi) * 1000 (millifurlong/furlong) * ...

The expression above converts miles per hour to millifurlongs per hour. Notice how the mi units cancel and the furlong units cancel. Tack on a few more units to get to millifurlongs/microfortnight.

 

[shortman12012]

if i take this and continue would the rest be
55 (mi/hr) * 8 (furlong/mi) * 1000 (millifurlong/furlong) * 336 (hours/fortnight) * 10^-6 (fortnight/microfortnight)?

 

[Mark44]

Yes, that looks good.

 

[shortman12012]

ahh thank you, that's the correct answer, thank you for your help :)

 

[Mark44]

Sure - you're welcome!