To learn how to convert the units, try here
.You should get 704 inches per second.
Given that value, and the radius of the wheel that the bike rides on, you can find the number of rotations needed
per second to get the required linear velocity: Divide the distance per second by the circumference, to find the number of circumferences (that is, the number of rotations) needed to cover that distance in a second.
I think you're supposed to assume that the small gear revolves in synch with the wheel, so you have that many revolutions per second for the small gear. Use the radius of the small gear to find the "distance" that the gear moves in that number of revolutions.
Then use the radius and circumference of the large gear to find the number of revolutions of the large gear. This will give you the revolutions per second.
Multiply by 60 to get the revolutions per minute. (I get the same answer as what you've been given.)