CAT is a national-level entrance exam conducted by the IIMs for the candidates aspiring to get admission into the IIMs and other top B-Schools. There are usually three sections in the CAT exam: Verbal Ability & Reading Comprehension, Quantitative Ability and Data Interpretation and Logical Reasoning. Time and Distance is an important part of the Quantitative Aptitude section. Here in this article some basic concepts have been discussed about Time and Distance.

**TIME AND DISTANCE – BASIC CONCEPTS**

The basic equation that will help you in solving time and speed sums is:

Speed = Distance / Time

It follows that:

Distance = Speed × Time and Time = Distance ÷ Speed

For example, if a man goes to a place 100 km away and takes 4 hours in doing so, his speed is 100/4 = 25 km/hour. Or, if a man goes crosses a street 600 m in 5 minutes, his speed is 600/5 = 120 metres per minute.

Conversely, if a man is going in a rickshaw at a speed of 10km/hour, and he reaches in 1 ½ hours, the distance he has travelled is 10 × 1.5 = 15 km.

Similarly, if a man has to cover a distance of 100 km to go to another town and he can get a bus that goes at 40 km/hour, he will take a total time of 100/40 = 2 ½ hours.

There are 3 variables, speed, time and distance. Mostly the problem is to find the third variable where two are provided. The student must take care to convert the units. However, remember to convert the units from km/hour to metres/second and vice versa as the case may be.

These concepts are used inter-changeably but the basic equation is the same.

**Time Saver**

Speed and time have an inverse relationship. Therefore, if the speed becomes, say ½ times the original speed, then the time taken becomes double that of the original for the same distance.

Or, if the ratio of the speed of two moving objects is in the ratio of 3:4, the time taken by them to cover identical distance will be in the ratio of 4:3.

Remember that, while solving sums, units should be the same.

**Conversion of Units**

• To convert km/hour to metres per second, multiply by 5/18.

• To convert metres/second to km/hour, multiply by 18/5.

**Illustration 1:** What is the distance covered by a car traveling at a speed of 40 kmph in 15 minutes?

(Note that the speed is given in hours and time is in minutes)

**Solution:**

Distance = speed × time = 40 × 15/60 = 10 km.

Note that we must convert minutes into hours to get the answer.

**Illustration 2:** A man covers 75 km in 90 minutes. What is his speed in km/h?

**Solution:**

Speed = Distance ÷ Time. Since time is given in minutes and the required answer is in km/h, we need to convert time into equivalent hours.

90 minutes = 90/60 hours, hence speed = distance/time = 75 ÷ 90/60 = 75 × 60/90 = 50 km/h.

**Illustration 3:** A cyclist rides along a track of 21 km in 4 hrs. What is his speed in m/s?

**Solution:**

Speed in kmph = 21/4.

To convert to m/s, multiply by 5/18, hence 21/4 × 5/18 = 35/24 m/s.

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**Illustration 4:** A speed of 22.5 m/sec. is the same as:

1. 40.5 km/hr 2. 81 km/hr 3. 36.8 km/hr 4. 72 km/hr

**Solution:**

To convert m/s to km/h we must multiply by 18/5. 22.5 m/s is same as writing 45/2

Hence 45/2 × 18/5 = 81 km/hour.

**Illustration 5:** A man covers 75 kms in 90 minutes. What is his speed in km/h?

**Solution:**

Speed = Distance ÷ Time. Since time is given in minutes and the required answer is in km/h, we need to convert time into equivalent hours.

90 minutes = 90/60 hours, hence speed = distance/time = 75 ÷ 90/60 = 75 × 60/90 = 50 km/h.

**Illustration 6:** A bowler has a run-up of 100m and the speed with which he runs is estimated to be 36 km/hour. How much time does he take to complete his run up?

**Solution:**

First we convert the speed into m/s since the distance is given in metres. 36 km/hr = 36 × 5/18 = 10 m/s.

Time taken = D/S = 100/10 = 10 seconds.

**Basic Concepts:**

(i) Speed = Distance/Time

(ii) Time = Distance/Speed

(iii) Distance = (Speed × Time).

(iv) If a certain distance is covered at x km/hr and the same distance is covered at y km/hr, then the average speed during whole journey is [2xy/(x + y)] km/hr

(v) If the speed of a body is changed in the ratio a : b, then the ratio of the time taken changes in the ratio b : a.

(vi) x km/hr = (x × 5/18) m/sec.

(vii) x metres/sec. = (x ×18/5) km/hr.

**Illustration 7:** An aeroplane coves a certain distance at a speed of 240 km per hour in 5 hours. To cover the same distance in 1 2/3

hours, it must travel at a speed of

1. 300 km/hr. 2. 360 km/hr. 3. 600 km/hr. 4. 720 km/hr.

**Solution:**

First find distance = 240 × 5 = 1200 km.

New time = 5/3 hours.

Speed = D/T = 1200 × 3/5 = 720 km/hr

**Illustration 8:** A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 42 minutes, will be covered by A in:

1. 14 min 2. 28 min 3. 63 min 4. 7 min

**Solution:**

If C has a speed of x km/hr, B has 3x and A has 6x, according to the sum. Ratio of the speeds is 1 : 3 : 6

(If the speed of a body is changed in the ratio a : b, then the ratio of the time taken changes in the ratio b : a.) Hence the ratio of time is 6 : 3 : 1.

C takes 42 minutes, hence 6x = 42, or x = 7. Hence A should take 7 minutes.

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