Question

1. a clever octopus swims 8¼ km at a speed of 0.5 km/h. how long does the octopus take to swim this distance in hours and minutes?

Explanation:

Step1: Recall the formula for time

The formula relating distance \(d\), speed \(v\), and time \(t\) is \(t=\frac{d}{v}\). Here, the distance \(d = 8\frac{1}{4}\space km=\frac{33}{4}\space km\) (since \(8\frac{1}{4}=\frac{8\times4 + 1}{4}=\frac{33}{4}\)) and the speed \(v = 0.5\space km/h=\frac{1}{2}\space km/h\).

Step2: Calculate the time in hours

Substitute the values of \(d\) and \(v\) into the formula: \(t=\frac{\frac{33}{4}}{\frac{1}{2}}\). When dividing by a fraction, we multiply by its reciprocal, so \(t=\frac{33}{4}\times2=\frac{33}{2}=16.5\) hours.

Step3: Convert the decimal part to minutes

The decimal part of the time in hours is \(0.5\) hours. Since \(1\) hour \( = 60\) minutes, we convert \(0.5\) hours to minutes by multiplying by \(60\): \(0.5\times60 = 30\) minutes.

Step4: Combine hours and minutes

The total time is \(16\) hours and \(30\) minutes.

Answer:

The octopus takes 16 hours and 30 minutes.