7. Determine the equivalent rates. a) 4laps/15min=12laps/ldots min b) 20km/5h=km/h c) 10m/30sec=m/min d) 20km/15min=km/h

## Step 1: Finding the Multiplier for (a)<br />### We have $4$ laps in $15$ minutes. We want to find how many minutes it takes for $12$ laps. Since $12 = 4 \times 3$, we multiply the time by $3$ as well. $15 \text{ min} \times 3 = 45 \text{ min}$.<br /><br />## Step 2: Calculating the Unit Rate for (b)<br />### We have $20$ km in $5$ hours. To find the unit rate (km/h), we divide the distance by the time: $\frac{20 \text{ km}}{5 \text{ h}} = 4 \text{ km/h}$.<br /><br />## Step 3: Converting Seconds to Minutes for (c)<br />### We have $10$ meters in $30$ seconds. Since there are $60$ seconds in a minute, and $30$ seconds is $\frac{30}{60} = \frac{1}{2}$ of a minute, we have $10$ meters in $\frac{1}{2}$ minute. To find the rate in meters per minute, we multiply the distance by $2$: $10 \text{ m} \times 2 = 20 \text{ m/min}$. Alternatively, since $1 \text{ min} = 60 \text{ sec}$, we can set up a proportion: $\frac{10 \text{ m}}{30 \text{ sec}} = \frac{x \text{ m}}{60 \text{ sec}}$. Cross-multiplying gives $30x = 600$, so $x = 20$ m/min.<br /><br />## Step 4: Converting Minutes to Hours for (d)<br />### We have $20$ km in $15$ minutes. Since there are $60$ minutes in an hour, $15$ minutes is $\frac{15}{60} = \frac{1}{4}$ of an hour. We have $20$ km in $\frac{1}{4}$ hour. To find the rate in km/h, we multiply the distance by $4$: $20 \text{ km} \times 4 = 80 \text{ km/h}$. Alternatively, since $1 \text{ hr} = 60 \text{ min}$, we can set up a proportion: $\frac{20 \text{ km}}{15 \text{ min}} = \frac{x \text{ km}}{60 \text{ min}}$. Cross-multiplying gives $15x = 1200$, so $x = 80$ km/h.