If Jim drives \(k\) miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

[Gmat_mission]

If Jim drives \(k\) miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. \(\dfrac{500}{k}\)
B. \(\dfrac{k}{500}\)
C. \(60k\)
D. \(10k\)
E. \(\dfrac{50}{k}\)

[spoiler]OA=A[/spoiler]

Source: Princeton Review

[Brent@GMATPrepNow]

If Jim drives \(k\) miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. \(\dfrac{500}{k}\)
B. \(\dfrac{k}{500}\)
C. \(60k\)
D. \(10k\)
E. \(\dfrac{50}{k}\)

[spoiler]OA=A[/spoiler]

Source: Princeton Review

We can solve this question using equivalent ratios

Jim drives k miles in 50 minutes
We're comparing miles traveled to minutes elapsed.
Jim travels k miles for every 50 minutes.
Our ratio is k miles/50 minutes

How many minutes will it take him to drive 10 miles, at the same rate?
So, our ratio is 10 miles/? minutes

So, our equation is: k/50 = 10/?
Cross multiply to get: (?)(k) = (50)(10)
Simplify: (?)(k) = 500
Solve for ? to get: ? = 500/k

Answer: A

Cheers,
Brent