Math question help2!!!

<p>John can run uphill a distance of 500 yds in 8 min. He can run downhill a distance of 500 yds in 4 mins. What is his average speed for both the uphill and downhill trips?</p>

<p>***The answer sheet says it's 83.333 yds per minute.</p>

<p>PLEASE SHOW ME ALL THE STEPS! THANKS!</p>

<p>Total Rate = (Total Distance / Total Time)</p>

<p>The total distance traveled is 1000 yards (500 up + 500 down) and the total time is 12 minutes (8 up and 4 down).</p>

<p>Rate = (1000 yards / 12 minutes)
Rate = 88.333 yards/minute</p>

<p>@Yankeesfanatic</p>

<p>I have a question. I see where you came from. I'm not sure why this way doesn't make sense. Please correct me.</p>

<p>Uphill avg. speed= 500/8
Downhill avg. speed= 500/4</p>

<p>Avg. Uphill and Downhill speed=[(500/8)+(500/4)]/2=(62.5+125)/2=93.75 yd per min.</p>

<p>I think this totally makes sense too...</p>

<p>You can't take the average of the two rates because they were for unequal times.</p>

<p>Your method would work if he ran up and down for the same amount of time. For example, if he ran up for 300 yards in 8 minutes and down for 500 yards in 8 minutes:</p>

<p>Rate = Total Distance / Total Time
= (800 yards)/(16 minutes)
= 50 yards/minute</p>

<p>With your method:
[(500/8) + (300/8)] / 2 = (62.5 + 37.5) /2 = 50 yards/minute</p>

<p>I can't explain it better than that the rates were not for equal times so you cannot just take an average. You have to add up the total distance and total time and use R = D/T.</p>

<p>@cocali619
I think we can use V(average) = (V1+V2)/2 equation only if the acceleration is constant -- we will get a straight V graph when a is constant. As the question doesn't mention anything about the a, we should use V(average) = Total Distance / Total Time. </p>

<p>yankeesfanatic's equal time method work because the time is same for both uphill and downhill. We can get total time by multiplying the denominator of (V1+V2) with denominator 2 of the V(average) equation. For example,
[(500/8) + (300/8)] / 2 = (500+300)/8 * 2, then we get,
(500+300)/16, which is the equation we will get by using V(average) = Total Distance / Total Time. Hope this helps! :-)</p>

<p>it's easy
just (500+500)/(4+8)
the result is 83.333</p>