## Time, Speed and Distance Problem with Explanations:

Time, Speed and Distance is an important topic for all competitive exams. At least 2-3 problems are come from Train problems(Time, Speed and Distance) chapter in all competitive exams like SSC and bank exams (SBI and IBPS-clerk and PO). This section will teach you to understand Time, Speed and Distance formulas to solve problems quickly.

**Time, Speed and Distance- Study material for all competitive exams**

Speed, Distance and Time is a part of quantitative or numerical aptitude section for all competitive exams. This chapter will give brief explanation to Time, Speed and Distance Problems. This will be helpful to crack all competitive exams with more marks. “Practice makes a man perfect” so please practice more problems with different models. All the best for your preparations and success.

### Formulas for Time, Speed and Distance:

#### Average Speed Formula

- Average speed =
**Total Distance covered/ Total Time Taken**

- When the distance is constant

**Average speed = 2xy/x+y**Where, x and y are the two speeds at which the same distance has been covered.

- When time taken is constant
**Average speed = (x + y)/2**Where, x and y are the two speeds at which we traveled for the same time.

**Time and Distance Formula**

**Distance = Speed × Time.**Using this formula, all basic problems can be handled. However, you need to make sure about the correct usage of units while using the above formulas.- Speed is inversely proportional to time taken when distance travelled is constant. So
**when speed increases, time decreases**and vice versa.

**Relative Speed**

- Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.

**Time, Speed and Distance Problems with Explanations for all competitive exams**

Before go through the problems of Time, Speed and Distance. Please understand and learn basic formulas of Time, Speed and Distance.

Please note question complexity is differ for each exams.

While learning solve high difficulty questions to boost your knowledge and success your exams.

#### Problems with Explanation:

**1) The distance between two stations A and B is 280 km. One train at a speed of 80 kmph leaves station A at 7:00 pm towards station B. Another train at a speed of 120 kmph leaves station B at 6:00 pm towards station A. Then at what time both trains meet?**

** A) 6:50 pm**

** B) 7:48 pm**

** C) 10:40 pm**

** D) 9:20 pm**

** E) None of these**

Explanation:

First train speed = a ; Second train speed = b

Time taken to meet = (Distance (+/-) t(b))/Relative Speed

If the second train started before the first train then [-t]
Time taken to meet = (Distance – t(b))/Relative Speed

Time taken to meet = (280 – 1(120))/200 = 48 minutes

Time both trains meet at = 7.00 pm + 48 minutes = 7:48 pm

** 2) The distance between two stations P and Q is 250 km. A train leaves P towards Q at 80 kmph. After half an hour another train leaves Q towards P at 120 kmph. Find the distance of the point where the two trains meet, from P.**

** A) 132 km**

** B) 145 km**

** C) 128 km**

** D) 124 km**

** E) None of these**

Explanation:

The distance of the point where the two trains meet is “x”

x/80 – (250 – x)/120 = 1/2

3x – 2(250 – x) =1/2 * 240

3x – 500 + 2x = 120

5x = 620

x = 124 km.

**3) The distance between two stations P and Q is 240 km A train starts from P towards Q and another train from Q to P at the same time and they meet after 8 hours. The train travel traveling from P to Q is slower by 6 kmph compared to another train from B to A, then find the speed of the slower train?**

** A) 12 kmph**

** B) 15 kmph**

** C) 20 kmph**

** D) 13 kmph**

** E) None of these**

**Explanation:**

Speed of slower train = x

Speed of faster train = x+6

Relative speed = 2x + 6

240/2x + 6 = 8

240 = 16x – 48

16x = 192

x = 12 kmph

**4) A train covers the distance between P and Q in 4 hours. If the speed is reduced by 4 kmph, then the same distance is covered in 5 hours. Find the speed of the train in Kmph?**

** A) 10 kmph**

** B) 15 kmph**

** C) 25 kmph**

** D) 18 kmph**

** E) 20 kmph**

Explanation:

d/x = 4

d/x-4 = 5

4x = 5x – 20

x = 20 kmph

**5) A train covers the distance between P and Q in 5 hours. If the speed is reduced by 5 kmph, then the same distance is covered in 6 hours. Find the reduced speed and distance between P and Q in km?**

** A) 10 kmph; 100 km**

** B) 15 kmph; 120 km**

** C) 30 kmph; 150 km**

** D) 18 kmph; 120 km**

** E) 25 kmph; 150 km**

Explanation:

d/x = 5

d/x-5 = 6

5x = 6x – 30

x = 30 kmph

Reduced speed = x -5 = 30 – 5 = 25 kmph

d = 150

**6) Vimal completes the first part of his journey at 30kmph and the next at 60kmph, covering the entire journey at an average speed of 40 kmph. What is the ratio of the distance that he covered at 30kmph to that he covered at 60kmph?**

** A) 2 : 1**

** B) 1 : 5**

** C) 3 : 1**

** D) 3 : 5**

** E) None of these**

Explanation:

Distance of first part of his journey = x

Distance of first part of his journey = y

x/30 + y/60 = (x + y)/40

6x + 2y = 3x + 3y

x/y = 3:1

**7) Suresh takes 7 hours 40 minutes in walking to a certain place and riding back. If he walks on both ways he will lose one hour. The time he would take to ride both ways is?**

** A) 5 hours 20 minutes**

** B) 7 hours 40 minutes**

** C) 6 hours 20 minutes**

** D) 6 hours 40 minutes**

** E) None of these**

Explanation:

Walking + Riding = 7 hours 40 minutes

Walking + Walking = 8 hours 40 minutes

So Walking = 4 hours 20 minutes

Riding + Riding = 6 hours 40 minutes

**8) Anil completed his journey in 10 hours. He travels first half of the journey at the rate of 22 kmph and second half at the rate of 18 kmph. Find the total journey in km.**

** A) 145 km**

** B) 198 km**

** C) 220 km**

** D) 180 km**

** E) None of these**

Explanation:

Total hours = 10 hours

Average Speed = 2xy/(x+y) = 2*22*18/(40) = 19.8 kmph

Total Journey in Km = 19.8 * 10 = 198 km

**9) Two cars start from a place with a speed of 40 kmph at an interval of 10 minutes. What is the speed of a man coming from the opposite direction towards the place if he meets the cars at an interval of 8 minutes?**

** A) 10 kmph**

** B) 13 kmph**

** C) 14 kmph**

** D) 16 kmph**

** E) None of these**

Explanation:

Distance covered in 10 minutes at 60 kmph = distance covered in 8 minutes at (60+x) kmph.

40*10/60 = 8/60 * (40+x)

20 * 5 = 80 + 2x

x = 10 kmph

**10) Waking 3/4 of his normal speed, Ravi was 18 minutes late in reaching his office. The usual time took to cover the distance between his home and office was:**

** A) 36 minutes**

** B) 24 minutes**

** C) 42 minutes**

** D) 54 minutes**

** E) None of these**

** ****Explanation:**

3/4 of speed = 4/3 of original time

4/3 of original time = original time + 18 minutes;

1/3rd of original time = 18 minutes;

Thus, original time = 18*3 = 54 minutes.