To compress spring 1 by 0.20m takes 150j of work. stretching spring by 2 by 0.30 m requires 210j of work. which spring is stiffer?

Work to stretch the a spring is found by the equation 1/2kx^2 where k is the spring constant and x is the distance stretched or compressed. so just fill in the numbers to solve and see which spring has a higher k=spring constant. so for spring 1 we have 1/2kx^2=150j which gives 1/2k (.20m^2) = 150j and solving for k we get k=7500, for spring 2 we have 1/2kx^2=210j which gives the equation 1/2k (.30m^2) = 210j which gives k=4666.67 so spring 1 has a much spring higher spring constant so spring 1 is stiffer which means it takes more force to stretch or compress.