Bunuel wrote:
Running on a 10-mile loop in the same direction, Sue ran at a constant rate of 8 miles per hour and Rob ran at a constant rate of 6 miles per hour. If they began running at the same point on the loop, how many hours later did Sue complete exactly 1 more lap than Rob?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
As I mention in the video below, we can often solve these kinds of problems using more than 1 approach.
So, instead of comparing distances (as I did above), let's compare
timesOur word equation can be:
Sue's travel time =
Rob's travel time Let
x = the distance Rob traveled
We know that Sue traveled ONE LAP more than Rob traveled. Since 1 lap = 10 miles, we know that Sue traveled 10 miles MORE THAN Rob.
This means
x + 10 = the distance Sue traveled
time = distance/speedSo, our word equation becomes:
(x + 10)/8 =
x/6Cross multiply to get: 6(x + 10) = 8(x)
Expand to get: 6x + 60 = 8x
We get: 60 = 2x
So, x = 30
This means ROB traveled 30 miles (and it means SUE traveled 40 miles)
If they began running at the same point on the loop, how many hours later did Sue complete exactly 1 more lap than Rob?time = distance/speedLet's use Rob's distance and speed to get: time = 30/6 = 5 hours
Answer: C
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[youtube]https://www.youtube.com/watch?v=avDLan39jqs[/youtube]