The Formula
Distance = Rate × Time → d = r × t
This one formula rearranges to solve for any of the three values:
Distance: d = r × t
Rate (speed): r = d ÷ t
Time: t = d ÷ r
Examples
Find distance: A car drives 55 mph for 3 hours
d = r × t = 55 × 3 = 165 miles
Find rate: You traveled 200 miles in 4 hours
r = d ÷ t = 200 ÷ 4 = 50 mph
Find time: How long to drive 300 miles at 60 mph?
t = d ÷ r = 300 ÷ 60 = 5 hours
Watch the Units
Units must match. If speed is in miles per hour, time must be in hours — not minutes. Convert first if needed.
A car goes 45 mph for 30 minutes
Convert: 30 minutes = 0.5 hours
d = 45 × 0.5 = 22.5 miles
💡 Memory trick: Think of the "DRT triangle." Cover the variable you need: cover D and you see R×T. Cover R and you see D÷T. Cover T and you see D÷R.
🎯 Practice Problems
1. A train travels at 80 mph for 2.5 hours. How far does it go?
A) 160 miles
B) 180 miles
C) 200 miles
D) 320 miles
2. You drove 150 miles in 3 hours. What was your average speed?
A) 45 mph
B) 50 mph
C) 53 mph
D) 450 mph
3. How long does it take to drive 240 miles at 60 mph?
A) 3 hours
B) 4 hours
C) 6 hours
D) 14,400 hours
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🎯 Bonus Practice
1. A cyclist rides 12 mph for 45 minutes. How far?
A) 6 miles
B) 9 miles
C) 12 miles
D) 540 miles
2. A plane flies 2,400 miles in 4 hours. What is its speed?
A) 400 mph
B) 600 mph
C) 800 mph
D) 9,600 mph
3. At 65 mph, how long to drive 325 miles?
A) 4 hours
B) 5 hours
C) 6 hours
D) 6.5 hours
4. A runner goes 6 miles in 48 minutes. What is the speed in mph?
A) 6 mph
B) 7.5 mph
C) 8 mph
D) 10 mph
5. Two cars leave at the same time. Car A goes 50 mph, Car B goes 70 mph. After 3 hours, how much farther is Car B?
A) 20 miles
B) 40 miles
C) 60 miles
D) 90 miles