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In this module we will deal with basic concepts of time and distance, speed, average speed, conversion from km/h to m/s and vice versa. This chapter will form the basis of further concept of relative speed which is used in train and boat problems.

**Important Formulas**

- Speed=Distance/Time
- Distance=Speed × Time
- Time=Distance/Speed
- To convert Kilometers per Hour(km/hr) to Meters per Second(m/s) x km/hr=(x×5)/18m/s
- To convert Meters per Second(m/s) to Kilometers per Hour(km/hr) x m/s=(x×18)/5 km/hr
- If a car covers a certain distance at x kmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/(x+y) kmph
- Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝ 1/Time (when distance is constant)
- If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is 1/a:1/b or b : a

__Solved Examples__

| |

A. 8.2 | B. 4.2 |

C. 6.1 | D. 7.2 |

**Answer : **Option D

**Explanation :**

Distance = 600 meter

time = 5 minutes = 5 x 60 seconds = 300 seconds

Speed = distance/time=600/300=2m/s=(2×18)/5 km/hr=36/5 km/hr=7.2 km/hr

| |

A. 17 hr | B. 14 hr |

C. 12 hr | D. 19 hr |

**Answer : **Option A

**Explanation :**

Relative speed = 5.5 - 5 = .5 kmph (because they walk in the same direction)

distance = 8.5 km

Time = distance/speed=8.5/.5=17 hr.

| |

A. 1 hr 42 min | B. 1 hr |

C. 2 hr | D. 1 hr 12 min |

**Answer :** Option D

**Explanation :**

New speed = 6/7 of usual speed

Speed and time are inversely proportional.

Hence new time = 7/6 of usual time

Hence, 7/6 of usual time - usual time = 12 minutes

=> 1/6 of usual time = 12 minutes => usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes

| |

A. 3 km | B. 4 km |

C. 5 km | D. 6 km |

**Answer :** Option D

**Explanation :**

If a car covers a certain distance at x kmph and an equal distance at y kmph,the average speed of the whole journey = 2xy/(x+y) kmph

Hence, average speed = (2×3×2)/(2+3)=12/5 km/hr .

Total time taken = 5 hours

⇒Distance travelled = (12/5)×5=12 km

⇒Distance between his house and office =12/2=6 km

| |

A. 80 km | B. 70 km |

C. 60 km | D. 50 km |

**Answer :** Option D

**Explanation :**

Assume that the person would have covered x km if travelled at 10 km/hr

⇒Speed = Distance/Time=x/10..... (Equation1)

Give that the person would have covered (x + 20) km if travelled at 14 km/hr

⇒Speed = Distance/Time=(x+20)/14..... (Equation2)

From Equations 1 and 2,

X/10=(x+20)/14 ⇒14x=10x+200 ⇒4x=200 ⇒x=200/4=50

| |

A. 210 miles | B. 230 miles |

C. 250 miles | D. 260 miles |

**Answer : **Option B

**Explanation :**

Speed1 = 50 miles/hour

Time1 = 2*(1/2) hour=5/2 hour

⇒ Distance1 = Speed1 × Time1 = (50×5)/2=25×5=125 miles

⇒Speed2 = 70 miles/hour

Time2 = 1*1/2 hour=3/2 hour

Distance2 = Speed2 × Time2 = 70×3/2=35×3=105 miles

Total Distance = Distance1 + Distance2 =125+105=230 miles

| |

A. 1800 ft | B. 2810 ft |

C. 3020 ft | D. 2420 ft |

**Answer : **Option D

**Explanation :**

Speed of the sound = 1100 ft/s ⇒Time = ^{11}/_{5} second

Distance = Speed × Time = 1100 ×11/5=220×11=2420 ft

| |

A. 1250 | B. 1280 |

C. 1320 | D. 1340 |

**Answer : **Option A

**Explanation :**

Speed = 5 km/hr

Time = 15 minutes = 1/4 hour

Length of the bridge = Distance Travelled by the man

= Speed × Time = 5×1/4 km

=5×1/4×1000 metre=1250 metre

| |

A. 11 hrs | B. 8 hrs 45 min |

C. 7 hrs 45 min | D. 9 hts 20 min |

**Answer : **Option C

**Explanation :**

Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back

From this, we can understand that time needed for riding one way = time needed for waking one way - 2 hours

Given that time taken in walking one way and riding back = 5 hours 45 min

Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

In fact, you can do all these calculations mentally and save a lot of time which will be a real benefit for you.

| |

A. 121 km | B. 242 km |

C. 224 km | D. 112 km |

**Answer** : Option C

**Explanation** :

distance = speed x time

Let time taken to travel the first half = x hr

then time taken to travel the second half = (10 - x) hr

Distance covered in the first half = 21x

Distance covered in the second half = 24(10 - x)

But distance covered in the first half = Distance covered in the second half

=> 21x = 24(10 - x) => 21x = 240 - 24x => 45x = 240 => 9x = 48 => 3x = 16 ⇒x=16/3

Hence Distance covered in the first half = 21x=21×16/3=7×16=112 km. Total distance = 2×112=224 km

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