The Relationship Between Power Consumption and Electricity Usage

Problem Statement

Person A decided to investigate the relationship between the power consumption of an electrical appliance and the amount of electrical energy consumed.

(1) A fan with an average power consumption of $P_0$P0​ was used for a time $T_0$T0​. How much electrical energy, in $\mathrm{J}$J, did the fan consume during this time?

(2) An air conditioner with an operating current of $I_1$I1​ and a voltage of $V_1$V1​ was used for a time $T_1$T1​. What is the average power consumption of this air conditioner in $\mathrm{W}$W?

(3) In the case described in (2), how much electrical energy did the air conditioner consume in $\mathrm{J}$J?

Constraints

• $P_0 = 50\ \mathrm{W}$P0​=50 W
• $T_0 = 5400\ \mathrm{s}$T0​=5400 s
• $I_1 = 20\ \mathrm{A}$I1​=20 A
• $V_1 = 200\ \mathrm{V}$V1​=200 V
• $T_1 = 1.30 \times 10^5\ \mathrm{s}$T1​=1.30×105 s

Input Format

Let the answer to Part (1) be $A_1\ \mathrm{J}$A1​ J, the answer to Part (2) be $A_2\ \mathrm{W}$A2​ W, and the answer to Part (3) be $A_3\ \mathrm{J}$A3​ J. The dimensionless ratio $\frac{A_3}{A_1 \times A_2}$A1​×A2​A3​​ is expressed as the irreducible fraction $\frac{p}{q}$qp​. Find the values of $p$p and $q$q.