A dog, Bowser, and a cat, Mouser, live in the same house. Their kibble (dry pet food) has the same size pieces. Bowser is fed 120 pieces of kibble at a time and eats at the rate of 20 pieces of kibble in 20 seconds. Mouser is fed 40 pieces of kibble at a time and eats at the rate of 2 pieces of kibble in 20 seconds. If both pets start to eat at 6:30:00 a.m., at what time does Bowser finish his kibble and start to 'help' Mouser eat his kibble?

To solve the problem, we need to determine how long it takes for Bowser to finish his kibble and then find the time at which he starts helping Mouser. ### Step 1: Calculate Bowser's eating time Bowser is fed 120 pieces of kibble and eats at a rate of 20 pieces in 20 seconds. First, we find Bowser's eating rate in pieces per second: \[ \text{Bowser's rate} = \frac{20 \text{ pieces}}{20 \text{ seconds}} = 1 \text{ piece/second} \] Now, we calculate the total time it takes for Bowser to finish 120 pieces: \[ \text{Time for Bowser} = \frac{120 \text{ pieces}}{1 \text{ piece/second}} = 120 \text{ seconds} \] ### Step 2: Convert Bowser's eating time to minutes 120 seconds is equivalent to: \[ \frac{120 \text{ seconds}}{60 \text{ seconds/minute}} = 2 \text{ minutes} \] ### Step 3: Determine the finishing time for Bowser Bowser starts eating at 6:30:00 a.m. and takes 2 minutes to finish. Therefore, the time at which Bowser finishes eating is: \[ 6:30:00 \text{ a.m.} + 2 \text{ minutes} = 6:32:00 \text{ a.m.} \] ### Step 4: Calculate Mouser's eating time Mouser is fed 40 pieces of kibble and eats at a rate of 2 pieces in 20 seconds. First, we find Mouser's eating rate in pieces per second: \[ \text{Mouser's rate} = \frac{2 \text{ pieces}}{20 \text{ seconds}} = 0.1 \text{ pieces/second} \] Now, we calculate the total time it takes for Mouser to finish 40 pieces: \[ \text{Time for Mouser} = \frac{40 \text{ pieces}}{0.1 \text{ pieces/second}} = 400 \text{ seconds} \] ### Step 5: Convert Mouser's eating time to minutes 400 seconds is equivalent to: \[ \frac{400 \text{ seconds}}{60 \text{ seconds/minute}} \approx 6.67 \text{ minutes} \text{ (or 6 minutes and 40 seconds)} \] ### Step 6: Determine the finishing time for Mouser Mouser starts eating at the same time as Bowser, which is 6:30:00 a.m. Therefore, the time at which Mouser finishes eating is: \[ 6:30:00 \text{ a.m.} + 6 \text{ minutes and } 40 \text{ seconds} = 6:36:40 \text{ a.m.} \] ### Conclusion Bowser finishes his kibble at 6:32:00 a.m. and starts to help Mouser eat his kibble at that time. Therefore, Bowser will start helping Mouser at 6:32:00 a.m.