Question Number 112507 by bemath last updated on 08/Sep/20
Answered by mr W last updated on 09/Sep/20
$$\frac{\mathrm{1}}{{A}}+\frac{\mathrm{1}}{{B}}=\frac{\mathrm{1}}{\mathrm{35}} \\ $$$$\frac{\mathrm{5}}{\mathrm{7}}{A}+\frac{\mathrm{2}}{\mathrm{7}}{B}=\mathrm{90} \\ $$$$\mathrm{5}{A}^{\mathrm{2}} −\mathrm{735}{A}+\mathrm{630}×\mathrm{35}=\mathrm{0} \\ $$$${A}=\frac{\mathrm{735}\pm\mathrm{315}}{\mathrm{10}}=\mathrm{105}\:{or}\:\mathrm{42} \\ $$$${B}=\mathrm{52}.\mathrm{5}\:{or}\:\mathrm{210} \\ $$$$ \\ $$$${A}\:{can}\:{do}\:{the}\:{work}\:{in}\:\mathrm{105}\:{days}\:{or}\:\mathrm{42} \\ $$$${days}. \\ $$