If a train travels 75 mi/hr, how far...

Question

If a train travels 75 mi/hr, how far will it travel in 75 minutes?

How many hours does it take to travel 387 miles?

Answer 1

well if you set up your equations, 75/60 = X/75, now cross multiply. 75 * 75 = 5625 and then divide by 60 = 93.75 miles. for the other, divide 387 miles by 75,a nd you will get 5.16 hrs.

Answer 2

The units of measure are important and by using the right units you can guarantee that you will get the right answer.  

Since you want to know how far it travels based on a time in minutes, let's put the rate of speed in minute measure.  We set the equation so that the hour in the denominator (the bottom part of the unit of rate measure) of the first term cancels out with the second term.  Since we need minutes in the denominator of the rate of speed, we divide by 60 minutes since it is equal to one hour:

75 mi/hr  ÃƒÂ· 60 min  =  1.25 mi/min

Now that we have the rate of speed in miles per minute, simply multiply by the time which will leave distance (the minute in the denominator of the first term cancels with the minute in the second term):

1.25 mi/min  X   75 min = 93.75 mi

The second question is another application of ratios using units of measure.  Since the result needs to be in hours and you have your original unit of measure in miles and hours (75 mi/hr), it is simply a question of how to use it.

The result needs to be in hours which is in the denominator of the 75 mi/hr.  The way to get the denominator to be the numerator is to divide it into another number and so divide 75 mi/hr into 387 mi:

387 mi ÷ 75 mi/hr =  5.16 hr