Time, Speed & Distance Mental Math

The Speed-Distance-Time Triangle

Three formulas:

• Distance = Speed × Time
• Speed = Distance ÷ Time
• Time = Distance ÷ Speed

Mental Math Shortcuts

Converting units:

• 60 mph for 1 hour = 60 miles
• 30 mph for 2 hours = 60 miles
• 60 mph for 30 minutes = 30 miles

Pattern: Divide by 2 for half time

Common Speed Conversions

Miles per hour to miles per minute:

• Divide by 60
• 60 mph = 1 mile per minute
• 30 mph = 0.5 miles per minute

Kilometers to miles (approximate):

• 1 km ≈ 0.6 miles
• 100 km ≈ 60 miles

Quick Calculations

Example: 45 mph for 20 minutes

• 20 min = 1/3 hour
• 45 × 1/3 = 15 miles

Example: 300 miles at 60 mph

• Time = 300 ÷ 60 = 5 hours

Example: 150 miles in 3 hours

• Speed = 150 ÷ 3 = 50 mph

Meeting Problems

Two cars approach from opposite directions:

• Combined speed = sum of both speeds
• Time to meet = distance ÷ combined speed

Example:

• Car A: 40 mph
• Car B: 50 mph
• Starting distance: 180 miles
• Combined speed: 90 mph
• Time to meet: 180 ÷ 90 = 2 hours

Relative Speed

Same direction:

• Relative speed = difference

Example: Fast car catches slow car

• Fast: 70 mph
• Slow: 60 mph (20 mile head start)
• Catching speed: 70 - 60 = 10 mph
• Time to catch: 20 ÷ 10 = 2 hours