<p>Bernardo drives to work at an average speed of 50 miles per hour and returns along the same route at an average speed of 25 miles per hour. If his total travel time is 3 hours, what is the total number of miles in the round-trip?</p>
<p>a) 225
b) 112.5
c) 100
d) 62.5
e) 50</p>
<p>The answer is C, but why?</p>
<p>Since he travels the same distance D for each trip the only other thing that differs is the time it takes to travel that distance. We know distance/time = speed.</p>
<p>So for the first trip t1=D/50 and for the second trip t2=D/25.
Since D/50=(1/2)(D/25), we can determine that t1=t2 /2, meaning the first trip was shorter than the second.</p>
<p>We also know that t1 + t2 = 3 hours
Making that substitution for t1, t2 + t2/2=3, and so 1.5t2=3, and t2=2 hours
Plugging t2 back into the equation for t1 we get t1= 2/2 = 1 hour.</p>
<p>From there, just multiply the times by the corresponding speeds to get (1)(50) + (2)(25) = 100 miles</p>
<p>Oh okay, thanks!</p>
<p>Hmm... I just did the problem and got a different answer. What am I doing wrong?</p>
<p>D=rt</p>
<p>d/r + d/r = t total so
x/50 + x/25 = 3</p>
<p>x + 2x /50 = 3
3x=150 x=50 ???</p>
<p>If I'm reading it correctly, the problem is you are assuming the times are the same by assigning x to time when in fact the two times are very different. There are supposed to be two different variables for time, one for the first trip and one for the second trip.</p>