Was given formula IMA(1) = (r of rear sprocket/r of front sprocket) * (r of pedal/r of wheel) If Rear sprocket = r of 5

1.Distance traveled will be equal to the circumference of the wheel times the number of the rotation of the wheels. Note that rear wheel is attached to the rear sprocket so they have the same angular velocity w. Rear sprocket is connected to front sprocket via chain. We have the the pedals on front sprocket so they turn at the same angular velocity as well.

So we have two angular velocities at front wf and at rear wr. Their linear velocity are the same so we can write

Vf = Vr = wf x rf = wr x rr

we get ;

wf/wr = rr/rf which is basically the first part of IMA(1). (r of rear sprocket/r of front sprocket)

since angular velocity of the pedal and the angular velocity of front sprocket are the same we can write;

wp/wr = rr/rf whic means if we turn the pedal 1 time rear wheel will turn rr/rf times. So distance traveled will be;

number of rotations of the pedal times rr/rf times the circumference of the rear wheel.

2. I think here the linear velocity of the gears is asked. This can be calculated by

V = wp x rf = 90 x 5.57 = 501 cm/min =5 m/min.