Distance, Rate and Time | CSE Reviewer

What Is Distance, Rate, and Time?

There are 3 important ideas:

• Distance = How far you went (like kilometers or miles)
• Rate = How fast you went (like km per hour or miles per hour)
• Time = How long it took (like hours or minutes)

These 3 are connected by a simple formula.

Tip: Think: Distance = how far, Rate = how fast, Time = how long.

Example: You drive 60 km in 2 hours.

Distance = 60 km
Time = 2 hours
Rate = how fast? (we will find this)

Distance is how far, rate is how fast, and time is how long. They are connected by a formula.

The Main Formula

The main formula connects distance, rate, and time:

Distance = Rate × Time

You can also write this formula in 2 other ways:

• To find Rate: \( \text{Rate} = \frac{\text{Distance}}{\text{Time}} \)
• To find Time: \( \text{Time} = \frac{\text{Distance}}{\text{Rate}} \)

Shortcut: Use D = R × T. If you need R, do D ÷ T. If you need T, do D ÷ R.

Example 1: Find distance. Rate = 50 km/h, Time = 3 hours.

Step 1: Use formula → Distance = Rate × Time
Step 2: Plug in → Distance = \(50 × 3\)
Step 3: Calculate → \(50 × 3 = 150\)

Answer: 150 km

Example 2: Find rate. Distance = 120 km, Time = 2 hours.

Step 1: Use formula → Rate = Distance ÷ Time
Step 2: Plug in → Rate = \(120 ÷ 2\)
Step 3: Calculate → \(120 ÷ 2 = 60\)

Answer: 60 km/h

Example 3: Find time. Distance = 200 km, Rate = 50 km/h.

Step 1: Use formula → Time = Distance ÷ Rate
Step 2: Plug in → Time = \(200 ÷ 50\)
Step 3: Calculate → \(200 ÷ 50 = 4\)

Answer: 4 hours

Remember this: D = R × T. To find R, do D ÷ T. To find T, do D ÷ R.

Finding Distance (D = R × T)

To find distance, multiply rate by time.

Step-by-step:

• Step 1: Write the formula → Distance = Rate × Time
• Step 2: Plug in the numbers you know
• Step 3: Multiply
• Step 4: Write answer with unit (km, miles, m)

Tip: Make sure rate and time use the same time unit. If rate is km/h, time must be in hours.

Example 1: A car goes 60 km/h for 4 hours. How far?

Step 1: Formula → Distance = Rate × Time
Step 2: Plug in → Distance = \(60 × 4\)
Step 3: Multiply → \(60 × 4 = 240\)

Answer: 240 km

Example 2: A runner goes 8 m/s for 30 seconds. How far?

Step 1: Formula → Distance = Rate × Time
Step 2: Check units → Rate is m/s, time is seconds → OK
Step 3: Plug in → Distance = \(8 × 30\)
Step 4: Multiply → \(8 × 30 = 240\)

Answer: 240 meters

To find distance, multiply rate by time. Make sure units match.

Finding Rate (R = D ÷ T)

To find rate, divide distance by time.

Step-by-step:

• Step 1: Write the formula → Rate = Distance ÷ Time
• Step 2: Plug in the numbers you know
• Step 3: Divide
• Step 4: Write answer with unit (km/h, mph, m/s)

Tip: Rate is always "per hour" or "per second" or "per minute." Watch the unit.

Example 1: A plane travels 900 km in 3 hours. How fast?

Step 1: Formula → Rate = Distance ÷ Time
Step 2: Plug in → Rate = \(900 ÷ 3\)
Step 3: Divide → \(900 ÷ 3 = 300\)

Answer: 300 km/h

Example 2: You walk 10 km in 2.5 hours. How fast?

Step 1: Formula → Rate = Distance ÷ Time
Step 2: Plug in → Rate = \(10 ÷ 2.5\)
Step 3: Divide → \(10 ÷ 2.5 = 4\)

Answer: 4 km/h

To find rate, divide distance by time. Answer is in "per hour" or "per minute."

Finding Time (T = D ÷ R)

To find time, divide distance by rate.

Step-by-step:

• Step 1: Write the formula → Time = Distance ÷ Rate
• Step 2: Plug in the numbers you know
• Step 3: Divide
• Step 4: Write answer with unit (hours, minutes, seconds)

Tip: If answer is in decimals of an hour, convert to minutes. Multiply by 60.

Example 1: You drive 180 km at 60 km/h. How long?

Step 1: Formula → Time = Distance ÷ Rate
Step 2: Plug in → Time = \(180 ÷ 60\)
Step 3: Divide → \(180 ÷ 60 = 3\)

Answer: 3 hours

Example 2: A bike goes 45 km at 15 km/h. How long?

Step 1: Formula → Time = Distance ÷ Rate
Step 2: Plug in → Time = \(45 ÷ 15\)
Step 3: Divide → \(45 ÷ 15 = 3\)

Answer: 3 hours

Example 3: Convert decimal hours to minutes. Time = 2.5 hours.

Step 1: 0.5 hour = ? minutes
Step 2: Multiply by 60 → \(0.5 × 60 = 30\)

Answer: 2 hours and 30 minutes

To find time, divide distance by rate. If decimal hours, multiply by 60 to get minutes.

Two Objects Moving

Sometimes 2 objects move. There are 2 common cases:

• Same direction: Subtract rates to find the difference.
• Opposite direction: Add rates to find how fast they separate.

Shortcut: Same direction → subtract. Opposite direction → add.

Example 1: Same direction. Car A goes 60 km/h, Car B goes 40 km/h. How far apart after 2 hours?

Step 1: Subtract rates → \(60 - 40 = 20\) km/h (difference)
Step 2: Multiply by time → \(20 × 2 = 40\)

Answer: 40 km apart

Example 2: Opposite direction. Car A goes 50 km/h, Car B goes 70 km/h. How far apart after 3 hours?

Step 1: Add rates → \(50 + 70 = 120\) km/h (combined)
Step 2: Multiply by time → \(120 × 3 = 360\)

Answer: 360 km apart

Same direction → subtract rates. Opposite direction → add rates. Then multiply by time.

Tips and Shortcuts for Distance, Rate, Time

These problems can be fast if you use shortcuts. Here are the best tips.

Tips:

• Main formula D = R × T 
• To find D: multiply R × T
• To find R: divide D ÷ T
• To find T: divide D ÷ R
• Make sure units match (km/h with hours, m/s with seconds).
• Decimal hours to minutes: multiply by 60.
• Same direction → subtract rates.
• Opposite direction → add rates.

Shortcut: When driving, if you know distance and rate, time = distance ÷ rate. Example: 300 km at 60 km/h → \(300 ÷ 60 = 5\) hours.

More Practice Examples

Example 1: Rate = 40 km/h, Time = 5 hours. Find distance.
Step 1: D = R × T
Step 2: \(40 × 5 = 200\)
Answer: 200 km

Example 2: Distance = 150 km, Time = 3 hours. Find rate.
Step 1: R = D ÷ T
Step 2: \(150 ÷ 3 = 50\)
Answer: 50 km/h

Example 3: Distance = 240 km, Rate = 80 km/h. Find time.
Step 1: T = D ÷ R
Step 2: \(240 ÷ 80 = 3\)
Answer: 3 hours

Example 4: Convert 1.5 hours to hours and minutes.
Step 1: 0.5 × 60 = 30
Answer: 1 hour and 30 minutes

Example 5: Two cars go opposite. A = 60 km/h, B = 80 km/h. After 2 hours?
Step 1: Add rates → \(60 + 80 = 140\)
Step 2: Multiply by time → \(140 × 2 = 280\)
Answer: 280 km apart

What To Remember

• Distance = how far, Rate = how fast, Time = how long
• Main formula: D = R × T
• To find R: R = D ÷ T
• To find T: T = D ÷ R
• Make sure units match (hours with km/h, seconds with m/s)
• Decimal hours to minutes: multiply by 60
• Same direction → subtract rates
• Opposite direction → add rates

Multiple Choice Questions

Answer these in the comment section. Choose the best answer for each item.

1. A car goes 70 km/h for 4 hours. How far?

A. 240 km
B. 260 km
C. 280 km
D. 300 km

2. A plane travels 1,200 km in 3 hours. How fast?

A. 300 km/h
B. 350 km/h
C. 400 km/h
D. 450 km/h

3. You drive 200 km at 50 km/h. How long?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours

4. Convert 2.25 hours to hours and minutes.

A. 2 hours and 15 minutes
B. 2 hours and 25 minutes
C. 2 hours and 30 minutes
D. 2 hours and 45 minutes

5. Two cars go opposite. A = 50 km/h, B = 70 km/h. After 3 hours?

A. 300 km
B. 320 km
C. 340 km
D. 360 km