Lesson 1.8: Time, Speed, Distance

Introduction:
Time, Speed, and Distance problems are very common in SSC exams, especially in CGL and CHSL quantitative aptitude sections. These problems often involve trains, boats, and circular tracks.

1. Basic Formula

Speed=DistanceTime,Time=DistanceSpeed,Distance=Speed×Time\text{Speed} = \frac{\text{Distance}}{\text{Time}}, \quad \text{Time} = \frac{\text{Distance}}{\text{Speed}}, \quad \text{Distance} = \text{Speed} \times \text{Time}Speed=TimeDistance​,Time=SpeedDistance​,Distance=Speed×Time

• Units:

  • Distance: km or m

  • Time: hours or minutes

  • Speed: km/h or m/s

• Conversion:

1 m/s =3.6 km/h,1 km/h =518 m/s1 \text{ m/s } = 3.6 \text{ km/h}, \quad 1 \text{ km/h } = \frac{5}{18} \text{ m/s}1 m/s =3.6 km/h,1 km/h =185​ m/s

2. Average Speed

• Definition: When a body travels different distances at different speeds, the average speed is:

Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}Average Speed=Total TimeTotal Distance​

• Example:
  A car travels 60 km at 40 km/h and 60 km at 60 km/h.
  Time = 60/40 + 60/60 = 1.5 + 1 = 2.5 h
  Average speed = 120/2.5 = 48 km/h

3. Relative Speed

• Same direction:

Relative Speed=Speed1−Speed2\text{Relative Speed} = \text{Speed}_1 – \text{Speed}_2Relative Speed=Speed1​−Speed2​

• Opposite direction:

Relative Speed=Speed1+Speed2\text{Relative Speed} = \text{Speed}_1 + \text{Speed}_2Relative Speed=Speed1​+Speed2​

• Example:
  Train A = 60 km/h, Train B = 40 km/h (opposite) → Relative speed = 100 km/h

4. SSC Exam Tips

• Always convert units consistently.

• For trains crossing platforms:

Time to cross=Length of train + Length of platformSpeed\text{Time to cross} = \frac{\text{Length of train + Length of platform}}{\text{Speed}}Time to cross=SpeedLength of train + Length of platform​

• Boats: Speed downstream = Speed of boat + Speed of stream; Speed upstream = Speed of boat – Speed of stream.

• Practice average and relative speed formulas for speed tricks in SSC exams.

5. Practice Questions

1. A car travels 90 km at 30 km/h and 60 km at 60 km/h. Find average speed.

2. Two trains 100 m and 120 m long moving in opposite directions at 40 km/h and 60 km/h. Time to cross each other?

3. A boat can row at 10 km/h in still water. Stream speed = 2 km/h. Find downstream and upstream speed.

4. A man walks 5 km at 4 km/h and returns 5 km at 6 km/h. Find average speed for the round trip.

5. Train 200 m long moving at 72 km/h crosses a pole. Find time taken to cross.