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The distance, y, Miranda travels while cross-country skiing, y, her distance traveled, varies directly with the amount of time, x, that she skis. Suppose Miranda skis 10 miles (the y coordinate) in 2 hours (the x coordinate).
A. What is the speed in miles per hour that Miranda is traveling?

B. Use your answer for (A) to write a direct linear variation equation relating this information.

C. How far will Miranda go in 3 hours?

D. If she travels 20 miles, how long did she ski? This one is worked out backward, be careful!
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Respuesta :

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Using the principle of direct variation, the solution to the problem given are :

  • 5 miles per hour
  • d = 5t
  • 15 miles
  • 4 hours

Given the Parameters :

Distance = d

Amount of time = t

d α t ; d = kt

We can find k = constant of proportionality = speed of travel ;

d = 10 miles ; t = 2 hours

10 = 2k

k = 10/2

k = 5

Hence, speed = 5 miles per hour

B.) The direct linear variation expression becomes ;

d = 5t

C.) Distance traveled in 3 hours :

t = 3 hours

d = 5t

d = 5(3) = 15 miles

D. Time taken to travel a distance of 20 miles

d = 5t

20 = 5t

t = 20/5

t = 4 hours

Therefore, it will take 4 hours to travel a distance of 20 miles.

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