<p>I never know how to do these kind of questions</p>
<p>Mary drives from her house at 60 mph to school. she drives back home at 40 mph. Her total driving time is 1.5 hours. What is her avg speed?</p>
<p>can someone show me how to do these types of questions?</p>
<p>I don’t know what the formula is if the time is more than 1 hour, but here’s a simple system to solve it:</p>
<p>t1 + t2 = 1.5 hrs (equation 1)</p>
<p>60 * t1 = d
40 * t2 = d (equation 2)</p>
<p>60 * t1 = 40 * t2
t1 = t2 * 2/3</p>
<p>Plug in t1 in eq. 1 to solve for t2, then plug into eq. 2 to get the distance. speed = distance/time</p>
<p>I got 24 mph.</p>
<p>That can’t be right… how can the average speed of 60mph and 40mph be less than 40mph?</p>
<p>Can’t you use 2<em>S1</em>S2/S1+S2 for this and get 48 mph as the avg speed?</p>
<p>this is an easy problem because Mary is traveling the same distance back and forth. So you know if she traveled 80 mph one time and 40 mph another time that she spent 2 times longer going 40 mph than she did going 80 mph. So her going 40 mph took 1.5 times longer than it did her going 60 mph.</p>
<p>the problem is that you do not know the distance but you know the time. average velocity is total distance divided by total time. so you have to manipulate the relationship between the two times to find out the distance</p>
<p>t = time (hours) it took Mary going 60 mph
1.5t = time (hours) it took Mary going 40 mph (it took longer)
(t+1.5t) hours=1.5 hours
2.5t hours=1.5 hours
t = 1.5/2.5
1.5t=2.25/2.5</p>
<p>t = 1.5/2.5 = 0.6
1.5t=2.25/2.5 = 0.9</p>
<p>so she took 0.6 hours going 60 mph and 0.9 hours going 40 mph
she spent more time going the lower rate so the average rate is closer to 40 than it is 60, or somewhere in the lower half (40 to 50, as opposed to 50 to 60)</p>
<p>the distance is 0.6<em>60 or 0.9</em>40, both of which are 36. So total distance is 72, total time is 1.5 (given), and average velocity is 72/1.5=48 mph</p>
<p>Why is it that 1.5t = the time it took mary going 40 mph?</p>
<p>“So you know if she traveled 80 mph one time and 40 mph another time that she spent 2 times longer going 40 mph than she did going 80 mph. So her going 40 mph took 1.5 times longer than it did her going 60 mph.”</p>
<p>Where does the 80 mph come from?</p>
<p>60<em>t1=d
40</em>t2=d
60<em>t1=40</em>t2
t1=t2<em>2/3
1.5hr=90min
t1+t2=90
t1=90-t2
90-t2=t2</em>2/3
90=t2(2/3+1)
90=t2<em>5/3
t2=54
90-54=36=t1
60</em>(36/60)=36
40*(54/60)=36
36+36=72
72(m)/1.5(hr)=48mph</p>
<p>Same idea… but not as simple haha. Converted to minutes and then back. My mind is wired weird, idk.</p>
<p>2<em>S1</em>S2/S1+S2
(2* Speed 1 * speed 2) /(speed 1 + speed 2) = 48
the people showing off all that work ^ are just wasting time</p>