Soda Q is bottled at a rate of 500 liters/second, 24 hours a day. Soda V is bottled at a rate of 300 liters/second, 24 hours a day. If twice as many bottles of Soda V as of Soda Q are filled in a day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?
Accepted Solution
A:
Answer:[tex]\frac{10}{3}[/tex]Step-by-step explanation:Let x be the filled bottles of soda Q,As per statement,The filled bottles of soda V = 2x,Given,Rate of filling of soda Q = 500 liters per sec,So, the total volume filled by soda Q in a day = 500 × 86400 = 43200000 liters,( ∵ 1 day = 86400 second ),Thus, the volume of a bottle of Soda Q = [tex]\frac{\text{Total volume filled by soda Q}}{\text{filled bottles of soda Q}}[/tex][tex]=\frac{43200000}{x}[/tex]Now, rate of filling of soda V = 300 liters per sec,So, the total volume filled by soda V in a day = 300 × 86400 = 25920000 liters,Thus, the volume of a bottle of Soda V [tex]=\frac{25920000}{2x}[/tex]Thus, the ratio of the volume of a bottle of Soda Q to a bottle of Soda V [tex]=\frac{\frac{43200000}{x}}{\frac{25920000}{2x}}[/tex] [tex]=\frac{10}{3}[/tex]