SOLUTION: an athlete is 16 miles from home, running toward home at 6 mph. a)write a formula that calculates the distance D that the athlete is from home after X hours. b) determine D

Question 472166: an athlete is 16 miles from home, running toward home at 6 mph.
a)write a formula that calculates the distance D that the athlete is from home after X hours.
b) determine D when x=1.5 hours.
c) find X when D = 5.5 miles. interpret the results.
Answer by karaoz(32) (Show Source): You can put this solution on YOUR website!

Our hero athlete runs at 6 mph. This is hardly running but OK - there are all kinds of athletes.

The questions here requires understanding of the relationship between the distance, speed and time. The relationship is rather simple and it can be stated as Distance = Speed * Time. But because the branch of science that deals with these types of problems is physics then we should be polite enough to use their word for speed, which is velocity, and so this relationship, when only first letters of each word are used, is stated as d = vt. We will use this relationship to answer all the questions here.

a) Given: t = x hours; v = 6 mph. Write the formula for D.

Knowing D (distance from home) is equal to 16 miles less the distance covered by the athlete, we can write:
D = 16 - d.
But, we also know that
d = vt = 6x.
Using d = 6x, we can now write the expression for D in terms of x:
D = 16 - 6x
with the result being in miles

b) Given: x = 1.5 hours and v = 6 mph.
(Probably meaning that t = 1.5 hours since in the previous questions they said t = x hours. Strictly speaking if t = x hours and x = 1.5 hours then t = 1.5 hours hours, which is a very strange thing)

D = 16 - 6x = 16 - 6*1.5 = 9 (miles).

c) This time we know D, D = 5.5 miles and we do not know x, which again probably stands for time (t). Using the same formula (d = vt), we have:

5.5 = 16 - 6x, or
x = (16 - 5.5)/6 = 1.75 (hours)

Not very exciting result at all. What to interpret here? Well, remember the units! How long is one hour and what is 1.75 hours. We have minutes and we have 60 minutes in an hour. So, 0.75 of one hour is simply 45 minutes. What is then 1.75 hours? It is 1 hour and 45 minutes. So, in 1 hour and 45 minutes the athlete covered 10.5 miles (16 - 5.5) and the athlete is still 5.5 miles away from home.

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