Math / Numbers & Operations

QuestionExpress each rate in simplest form. a 10 km in 2 hours b $\$ 650$ for 13 hours c 2800 km in 20 days

Studdy Solution

STEP 1

1. Each rate is given in terms of a quantity per unit of time or cost.
2. The goal is to simplify each rate to its simplest form, meaning the smallest whole number ratio.

STEP 2

1. Simplify the distance rate.
2. Simplify the cost rate.
3. Simplify the travel rate.

STEP 3

For part (a), simplify the rate of $10$ km in $2$ hours.
Divide both the distance and the time by their greatest common divisor (GCD).
The GCD of $10$ and $2$ is $2$ .
$\frac{10 \text{ km}}{2 \text{ hours}} = \frac{10 \div 2 \text{ km}}{2 \div 2 \text{ hours}} = \frac{5 \text{ km}}{1 \text{ hour}}$

STEP 4

For part (b), simplify the rate of $\$650$ for $13$ hours.
Divide both the cost and the time by their greatest common divisor (GCD).
The GCD of $650$ and $13$ is $13$ .
$\frac{\$650}{13 \text{ hours}} = \frac{650 \div 13}{13 \div 13 \text{ hours}} = \frac{\$50}{1 \text{ hour}}$

STEP 5

For part (c), simplify the rate of $2800$ km in $20$ days.
Divide both the distance and the time by their greatest common divisor (GCD).
The GCD of $2800$ and $20$ is $20$ .
$\frac{2800 \text{ km}}{20 \text{ days}} = \frac{2800 \div 20 \text{ km}}{20 \div 20 \text{ days}} = \frac{140 \text{ km}}{1 \text{ day}}$
The simplified rates are: a. $5 \text{ km per hour}$ b. $\$50 \text{ per hour}$ c. $140 \text{ km per day}$

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