Time and Distance Questions

Here distance d = 800 mts

speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s

time t = 800x1860x5= 48 sec.

1. How to find Speed(s) if distance(d) & time(t) is given:

 Speed (S) = Distance (D)Time (T) 

Ex: Find speed if a person travels 4 kms in 2 hrs?

Speed = D/T = 4/2 = 2 kmph.

2.  Similarly, we can find distance (d)  if speed (s) & time (t) is given by

Distance (D) = Speed (S) x Time (T)

Ex : Find distance if a person with a speed of 2 kmph in 2 hrs?

Distance D = S X T = 2 x 2 = 4 kms. 

3.  Similarly, we can find time (t) if speed (s) &  distance (d) is given by

Time (T) = Distance (D)Speed (S)

Ex : Find in what time a person travels 4 kms with a speed of 2 kmph?

Time T = D/S = 4/2 = 2 hrs.

4. How to convert  km/hr into m/sec :

P km/hr = P x 518 m/sec

Ex : Convert 36 kmph into m/sec?

36 kmph = 36 x 5/18 = 10 m/sec 

5. How to convert  m/sec into km/hr :

P m/sec = P x 185 kmph.

Ex : Convert 10 m/sec into km/hr?

10 m/sec = 10 x 18/5 = 36 kmph.

6.  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 b : a.

7.  Suppose a man covers a certain distance at x km/ hr and an equal distance at y km/hr . Then, the average speed during the whole journey is 2xyx+y km/hr.

Let the initial speed of Akhil be '4p' kmph

Then speed after decrease in speed = '3p' kmph

We know that, 

Change in speed == Change in time

According to the given data,

$$\begin{gathered} 243p - 244p = 35 - 2560 \\ => p = 12 \end{gathered}$$

Hence, the initial speed of Akhil = 4p = 4 x 12 = 48 kmph.

Let the distance travelled by Tilak in first case or second case = d kms

Now, from the given data,

d/20 = d/22 + 36 min

=> d/20 = d/22 + 3/5 hrs

=> d = 132 km.

Hence, the total distance travelled by him = d + d = 132 + 132 = 264 kms.

Time taken to cover 600 km = 600/100 = 6 hrs.

Number of stoppages = 600/75 - 1 = 7

Total time of stoppages = 4 x 7 = 28 min

Hence, total time taken = 6 hrs 28 min.

Let the actual distance be t kms

Now, According to the data,

$$\begin{gathered} 5t + 860 = 6t \\ => 560t + 860 = 6t \\ => 60t + 8 = 72t \\ => 8 = 12t \\ => t = 8/12 = 2/3 hrs \end{gathered}$$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

We know 60 min = 1 hr
Total northward Laxmi's distance = 20kmph x 1hr = 20 km
Total southward Prasanna's distance = 30kmph x 1hr = 30 km
Total distance between Prasanna and Laxmi is = 20 + 30 = 50 km.

Speed of tractor = 360/12 = 30 kmph

Speed of jeep = 250 x 30/100 = 75 kmph

But, given ratio of speed of car, jeep and tractor is 3 : 5 : 2

Speed of car = 3 x 75/5 = 45 kmph

Required, average speed of car and jeep = 75 + 45/2 = 60 kmph.