<p>Jose left the White House and drove toward the recycling plant at an average speed of 40 km/h. Rob left some time later driving in the same direction at an average speed of 48 km/h. After driving for five hours Rob caught up with Jose. How long did Jose drive before Rob caught up?</p>
<p>Also how do you express this in algebra: Bob left x hours later? Is it t-x?</p>
<p>distance=rate<em>time (to “prove” this, km=(km/hr)</em>hr, where the hours cancel out to leave km=km).</p>
<p>So, we set up two equations. 1. distance for Jose, or DJ, eqauls speed Jose, or SJ, times time Jose, or TJ. So, DJ=SJ<em>TJ. You know the speed is 40. Say the time is t. So, DJ=40</em>t. 2. distance for Rob, or DR, eqauls speed Rob, or SR, times time for Rob, or TR. So, DR=SR<em>TR. Rob’s speed is 48, and his time is 5. So, DR=48</em>5=240 kilometres. </p>
<p>So, we know the distance Rob traveled after five hours. And since they were at the same distance at exactly 5 hours, the distance Rob traveled (240 km) is the same as the distance Jose traveled. So, recalling Jose’s equation from before, we have DJ=40<em>t. Since DJ is 240, we have 240=40</em>t, t=240/40=6 hours. So, Jose drived for 6 hours before Rob caught up.</p>
<p>Rob is 8km/hr faster than Jose. He drove for 5 hours. 8x5=40 means that Rob caught up 40 miles. Since Jose was driving at 40km/hr, it means Rob made up for an hour’s time.</p>
<p>5+1 = 6 hours</p>
<p>or 48 * 5 = 40 * X</p>
<p>^That’s the same as what I did, in case you didn’t read my post. And what is the purpose of providing a one-line answer? You should at least give an explanation of where the numbers all came from. Your one-line answer is leaving it up to the OP to put the pieces together, and that can lead to some confusion.</p>
<p>Thanks Grozza.</p>
<p>Also how do you express this in algebra: Bob left x hours later? Is it t-x?</p>
<p>Gamma, I felt my initial explanation was less mathematical and more clear than yours. Sorry if reposting the solution somehow offended (?) you</p>
<p>^It doesn’t really offend me. What really bothers me is that you didn’t really post the full solution. Presumably, you did some mental steps to get that equation down. This may be obvious for you, but it may not be for everyone else. The fact is, you can’t be sure how much the OP knows. And we are here to help the OP. So if you want to help out significantly more next time, post out the steps to get the answer (and read the other posts ;)). </p>
<p>And I don’t care about your first solution. You explained that. That is a good solution. I never thought of it that way. But, if you just posted “8*5=40=1 hour, so 5+1=6” I def. wouldn’t understand it, the OP probably wouldn’t, and the OP would lack one good solution for these problems. </p>
<p>OP: if t is the time that the two meet (and also the time since Jose left), and Bob left x hours after Jose, then Bob traveled for, yes, t-x hours.</p>