How far will you go if you go 50 mph for 105 minutes?

Answer 1

Here's a much shorter answer, showing the process to get there, with unit conversion in brackets:

50 [miles/hour] * 1/60 [hour/minutes] * 105 [minutes] = 50 / 60 * 105 [miles] =

87.5 [miles].

Read my original response for a more in-depth explanation of unit conversion.

-dluberger 09/02/2013

***Original Answer***

It is important to use proper unit conversion techniques here:

Speed is a scalar quantity expressed in distance-per-unit-time; since you want to end up with a distance in the same units as the speed, but your speed involves a different time unit, you must convert the given time to the same units, like so:

(50 miles / 1 hour) * (1 hour / 60 minutes) = (50 miles / 60 minutes) ; so divide 50 into 60, and leave the new units: [miles / minute], read "miles per minute". notice in the preceding equation, the first "fraction" has hours on the bottom (50 miles / 1 hour), and the next fraction has hours on the top (1 hour / 60 minutes). The reason we do this is because we want to know "If the resultant units must be in minutes, how do I express my speed in minutes?" To do so, we must somehow replace "hours" with minutes. The trick is to remember that a fraction with some number (or unit in this case) on the bottom, multiplied by a fraction with the samenumber on top causes that number to be cancelled.

So we get 50/60 miles-per-minute or 0.833 miles-per-minute. Now we can answer the original question:

(0.833 miles / 1 minute) * (105 minutes) : the minutes cancel, leaving only the unit miles: 0.833 miles * 105 = 87.5 miles

As a good excecise, take this technique of unit conversion, and try something like:

Given a speed of 50 mph (miles-per-hour), how many feet are travelled in 10 seconds?

Hint: you have to convert two units, not just one: miles to feet, and hours to seconds.

The answer is 733.33 feet. See if you can come up with the same answer.

-dluberger 4/10/2010