For every hour sue has a lead of \(\frac{2miles}{hr}\) over Rob.
To get an exact 1 lap lead sue has to have total lead of \(10\) miles as the lap is 10 miles long
Hence \(\frac{10}{2} = 5\). Time that is required to put a one lap lead on Rob
option c

When Sue completes exactly 1 more lap than Rob, she will have traveled exactly 10 miles more than Rob (since the loop is 10 miles long). We can let both of the times = t and create the equation:

8t = 6t + 10

2t = 10

t = 5

Answer: C

1 lap = 10 miles
So, if Sue completes 1 lap more than Rob completes, then we know that Sue has traveled 10 miles more than Rob

So, let's start with a word equation:
(Sue's travel distance) = (Rob's travel distance) + 10 miles

Distance = (speed)(time)
We know each person's speed, but we don't know their travel times.
Let t = Sue's travel time
So, t = Rob's travel time also

Now take our word equation and plug in the necessary values:
8t = 6t + 10
Solve to get: t = 5

Answer: C

I still have not been able to understand why the time would taken the same for both Sue and Rob, could anybody kindly advise?

They both started running at the same time, and we stopped the clock (for both runners) once Sue lapped Rob.

Cheers,
Brent

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 times

Our 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/speed
So, our word equation becomes: (x + 10)/8 = x/6
Cross 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/speed
Let's use Rob's distance and speed to get: time = 30/6 = 5 hours

Answer: C

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