Speed, Distance, and Time
Understanding speed, distance, and time is crucial for GMAT quantitative problems. These questions typically involve the formula:
Speed = Distance ÷ Time
This relationship can be rearranged as needed:
- Distance = Speed × Time
- Time = Distance ÷ Speed
Below, I’ll explain each concept with examples and strategies.
1. Key Formula and Units
Ensure consistency in units:
- Speed: kilometers/hour (km/h) or miles/hour (mph)
- Distance: kilometers (km) or miles (mi)
- Time: hours, minutes, or seconds
If units differ (e.g., speed in km/h, time in minutes), convert before calculations.
2. Types of Problems and Strategies
a. Direct Problems (Single Movement)
Example:
A car travels 150 km in 3 hours. What is its speed?
Solution:
Speed = Distance ÷ Time
= 150 ÷ 3 = 50 km/h
b. Two Objects Moving Toward Each Other
When two objects move toward each other, the relative speed is the sum of their speeds.
Example:
Two trains, Train A and Train B, are 300 km apart and travel toward each other at speeds of 80 km/h and 70 km/h, respectively. How long will it take for them to meet?
Solution:
Relative Speed = 80 + 70 = 150 km/h
Time = Distance ÷ Speed = 300 ÷ 150 = 2 hours
c. Catch-Up Problems (Overtaking)
When one object chases another, use the relative speed as the difference between their speeds.
Example:
Car A starts 2 hours earlier at 40 km/h. Car B starts later at 60 km/h. How long will it take Car B to catch Car A?
Solution:
Distance covered by Car A in 2 hours = 2 × 40 = 80 km
Relative Speed = 60 – 40 = 20 km/h
Time = Distance ÷ Speed = 80 ÷ 20 = 4 hours
d. Average Speed
For multiple trips at different speeds, use the formula:
Average Speed=Total DistanceTotal Timetext{Average Speed} = frac{text{Total Distance}}{text{Total Time}}
Example:
A car travels 60 km at 30 km/h and 90 km at 45 km/h. What is its average speed?
Solution:
Time for first part = 60 ÷ 30 = 2 hours
Time for second part = 90 ÷ 45 = 2 hours
Total Distance = 60 + 90 = 150 km
Total Time = 2 + 2 = 4 hours
Average Speed = 150 ÷ 4 = 37.5 km/h
e. Circular Tracks or Loops
When two objects travel on a circular track, calculate the time to meet based on their relative speed.
Example:
Two runners are on a circular track of 400 m. Runner A runs at 6 m/s, and Runner B runs at 4 m/s in the same direction. How long will it take for Runner A to overtake Runner B?
Solution:
Relative Speed = 6 – 4 = 2 m/s
Time = Distance ÷ Speed = 400 ÷ 2 = 200 seconds
3. Tips for GMAT Success
- Practice Word Problems: GMAT problems often disguise the formula in wordy scenarios. Practice identifying key data like speed, distance, and time.
- Understand Relative Speed: For moving toward each other, add speeds. For the same direction, subtract speeds.
- Estimate: GMAT is a timed test, so estimate when exact calculations aren’t necessary.
- Watch for Unit Conversions: Convert minutes to hours or vice versa when needed.
- Use Proportions: When variables change proportionally (e.g., speed doubles, time halves), use proportional reasoning instead of recalculating everything.
By mastering these types of problems and practicing regularly, you’ll approach GMAT speed, distance, and time questions with confidence.