Math Snap

STEP 1

1. We are asked to express given quantities as simplified rates.
2. We need to find average rates for given situations.
3. We need to compare earnings to determine who earns more.
4. We need to compare speeds in different units to determine which is faster.

STEP 2

1. Simplify given rates.
2. Calculate average rates.
3. Compare earnings.
4. Compare speeds.

STEP 3

a. Simplify the rate of students per bus.
$$\frac{180 \text{ students}}{3 \text{ buses}} = \frac{180}{3} = 60 \text{ students per bus}$$

STEP 4

b. Simplify the rate of dollars per kilogram.
\frac{\($\)5.60}{4 \text{ kg}} = \frac{5.60}{4} = \($\)1.40 \text{ per kg}

STEP 5

c. Simplify the rate of kilometers per hour.
Convert $2 \frac{1}{2}$ hours to an improper fraction: $2.5$ hours.
$$\frac{186 \text{ km}}{2.5 \text{ hours}} = \frac{186}{2.5} = 74.4 \text{ km per hour}$$

STEP 6

d. Simplify the ratio $5:2$.
The ratio $5:2$ is already in its simplest form.

STEP 7

a. Find the average rate of kilometers per day for Thelma.
$$\frac{8000 \text{ km}}{50 \text{ days}} = \frac{8000}{50} = 160 \text{ km per day}$$

STEP 8

b. Find the average rate of dollars saved per month for Callum.
\frac{\($\)1250}{6 \text{ months}} = \frac{1250}{6} \approx \($\)208.33 \text{ per month}

STEP 9

c. Find the average rate of growth per year for Ainslie.
Convert $2 \frac{1}{2}$ years to an improper fraction: $2.5$ years.
$$\frac{20 \text{ cm}}{2.5 \text{ years}} = \frac{20}{2.5} = 8 \text{ cm per year}$$

STEP 10

Compare Kelly's and Todd's earnings.
Kelly earns $\$96570$ per year.
Todd earns $\$7985$ per month, so annually he earns:
\($\)7985 \times 12 = \($\)95820 Kelly earns more than Todd by:
\($\)96570 - \($\)95820 = \($\)750

Compare speeds of $70 \text{ km/h}$ and $21 \text{ m/s}$.
Convert $70 \text{ km/h}$ to meters per second:
$$70 \text{ km/h} = \frac{70 \times 1000}{3600} \approx 19.44 \text{ m/s}$$ Since $21 \text{ m/s}$ is greater than $19.44 \text{ m/s}$, $21 \text{ m/s}$ is faster.
The solutions are:
1. Simplified rates:
- $60$ students per bus
- $\$1.40$ per kg
- $74.4$ km per hour
- Ratio $5:2$
2. Average rates:
- $160$ km per day
- $\$208.33$ per month
- $8$ cm per year
3. Kelly earns more than Todd by $\$750$.
4. $21 \text{ m/s}$ is faster than $70 \text{ km/h}$.