Question

Step 3a: Calculating the average rate

Answer 1

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Answer:

  a) average rate = (total distance)/(total time)

  b) Rave = 2·R1·R2/(R1 +R2)

  c) cheetah's average rate ≈ 50.91 mph

Step-by-step explanation:

a) Let AB represent the distance from A to B. Let t1 and t2 represent the travel times (in hours) on leg1 and leg2 of the trip, respectively. Then the distances traveled are...

  First leg distance: AB = 70·t1   ⇒   t1 = AB/70

  Second leg distance: AB = 40·t2   ⇒   t2 = AB/40

The average rate is the ratio of total distance to total time:

  average rate = (AB +AB)/(t1 +t2)

  average rate = 2AB/(AB/70 +AB/40) = 2/(1/70 +1/40) = 2(40)(70)/(70+40)

  average rate = 560/11 = 50 10/11 . . . mph

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No equations are given, so we cannot compare what we wrote with the given equations. In each step of the solution, we have used the rules of algebra and equality.

b) For two rates over the same distance (as above), the average is their harmonic mean:

  average rate = 2r1·r2/(r1+r2)

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c) The cheetah's average rate was 50 10/11 mph ≈ 50.91 mph.