A scientist is studying the motion of a particular glacier. He notes that this glacier has moved 2 over 3 of a meter in 3 over 4 of a day. What is the unit rate in meter(s)/day of this glacier?

The glacier has moved 2 over 3 of a meter in 3 over 4 of a day.Distance moved by glacier = 2 over 3 = 2/3 mDuration in which 2/3 distance was moved = 3 over 4 of a day = 3/4 daySo we have to find unit rate in meter(s)/day.Unit rate can be found by dividing distance moved by duration in which the distance was moved.So finding unit rate:[tex] Unit rate =\frac{distance moved}{duration} [/tex]We are given distance moved 2/3 and duration as 3/4.Plugging these values in the formula for unit rate,[tex] Unit rate =\frac{2/3}{3/4} [/tex]In division of fraction, we take reciprocal of second fraction and multiply it with the first.[tex] Unit rate =\frac{2}{3} *\frac{4}{3} [/tex]Unit rate = 8/9 m/dayAnswer : Unit rate at which glacier is moving is (8/9) meters per day.