elroy and herbert are product testers at a company that makes mouthwash. If elroy can complete a gargling cycle once every 20 seconds, and herbert can complete a gargling cycle once every 30 seconds, how many seconds will it take them to complete a combined total of 15 gargling cycles?

Answer 1

To determine how long it will take Elroy and Herbert combined to complete a total of 15 gargling cycles, let's first calculate how many cycles each of them can complete in one second.

• Elroy completes 1 cycle every 20 seconds, so in one second he completes: \[ \frac{1 \text{ cycle}}{20 \text{ seconds}} = 0.05 \text{ cycles per second} \]

• Herbert completes 1 cycle every 30 seconds, so in one second he completes: \[ \frac{1 \text{ cycle}}{30 \text{ seconds}} \approx 0.0333 \text{ cycles per second} \]

Next, we will add their rates of completing cycles: \[ \text{Combined rate} = 0.05 + 0.0333 = 0.0833 \text{ cycles per second} \]

Now, we need to find out how long it will take for them to complete a total of 15 cycles at their combined rate. Let \( t \) be the time in seconds needed to complete 15 cycles. We can set up the equation: \[ 0.0833 \cdot t = 15 \]

Now we can solve for \( t \): \[ t = \frac{15}{0.0833} \approx 180 \text{ seconds} \]

Therefore, it will take them approximately 180 seconds to complete a combined total of 15 gargling cycles.