Answer:
160 days
Explanation:
Using the equation
rA^3/TA^2 = rB^3/TB^2
Where rA is radius of Moon A = R
TA is Time for moon A complete one orbit = 20 days
rB is radius of Moon B =4R
TB is Time for moon B complete one orbit = ?
Therefore
rA^3/TA^2 = rB^3/TB^2
R^3/20^2 = (4R)^3/TB^2
Cross multiply to solve for TB, then we have
TB^2 × R^3 = (4R)^3 × 20^2
TB^2 × R^3 = 64 × R^3 × 400
TB^2 × R^3 = 25600 × R^3
Divide both sides by R^3
TB^2 = 25600
Square root both sides
TB = sqrt 25600
TB = 160days
