Question

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

Answer 1

(C) 5

Explanation:

Let x represent number of hours.

We have been given that running on a 10-mile loop in the same direction, Sue ran at a constant rate of 8 miles per hour.

Distance covered by Sue in x hours would be
`8x` miles.

We are also told that Rob ran at a constant rate of 6 miles per hour, so distance covered by Rob in x hours would be
`6x` miles.

Since Sue needs to complete one more loop than Rob, so difference of distances covered by Sue and Rob's in x hours should be equal to 10 miles.

We can represent this information in an equation as:

`8x-6x=10`

`2x=10`

`(2x)/(2)=(10)/(2)`

`x=5`

Therefore, 5 hours later Sue will complete exactly 1 more lap than Rob and option C is the correct choice.