**Finding the Speed When the Distance Traveled is Same :**

In this section, we will learn how to find the speed when the distance traveled is same.

The relationship between distance, speed and time.

Time = Distance / Speed

Speed = Distance / Time

Distance = Time ⋅ Speed

To convert minutes into hour, we should divide the given minutes by 60.

- If we want to convert the speed from km/hr to m/sec, we should multiply the speed by 5/18.
- If we want to convert the speed from m/sec to km/hr, we should multiply the speed by 18/5.

**Example 1 :**

Professor Greenberg traveled by scooter from his house to town that was some distance away. If he traveled at a constant speed of 50 km/hr, he would have arrived at 11 am. If he traveled at 75 km/hr, he would have arrived at 10 am. At what speed should he be riding if he wanted to arrive at 10.30 am.

**Solution :**

Even though the speed taken in both trips are different, he is covering the same distance.

Let A be the starting point and B be the ending point.

He is covering the distance from A to B at the speed of 50 km/hr.

He is covering the distance from B to A at the speed of 75 km/hr.

Time = Distance / Speed

Time taken at the speed 50 km/hr = Distance / 50 ---(1)

Time taken at the speed 75 km/hr = Distance / 75 ---(2)

If he traveled at the speed of 75 km/hr, he would have reached the destination 1 hour earlier.

The time difference is 1 hour.

(1) - (2)

1 = (D/50) - (D/75)

1 = (3D - 2D) / 150

150 = D

Distance covered is 150 km.

By applying the distance in (1), we get the time taken to travel from A to B.

Time = 150 / 50

Time = 3 hours

So, he is taking 3 hours to cover the distance 150 km. He started his travelling 3 hours before the 11 am. That is, he started his travel at 8 am.

According to the question, he needs to reach the destination at 10.30 am, that is he much reach the destination within 2 1/2 hours.

2 1/2 = 150 / speed

speed = 150 / (5/2)

Speed = 60 km/hr

Hence he should travel at the speed of 60 km/hr to reach the destination at 10.30 am.

**Example 2 :**

Mr Cartlan is driving from Red Deer to Okonagan for a business meeting. If he drives at a speed of 90 km/h, he will arrive at 4 pm. If he drives at a speed of 120 km/h, he will arrive 2 hours earlier. At what speed Mr Cartland be driving if he wants to arrive at 3.12 pm ?

**Solution :**

Even though the speed taken in both trips are different, he is covering the same distance.

Let A be the starting point and B be the ending point.

He is covering the distance from A to B at the speed of 50 km/hr.

He is covering the distance from B to A at the speed of 75 km/hr.

Time = Distance / Speed

Time taken at the speed 90 km/hr = Distance / 90 ---(1)

Time taken at the speed 120 km/hr = Distance / 120 ---(2)

If he traveled at the speed of 120 km/hr, he would have reached the destination 2 hours earlier.

The time difference is 1 hour.

(1) - (2)

2 = (D/90) - (D/120)

2 = (4D - 3D) / 360

720 = D

Distance covered is 720 km.

By applying the distance in (1), we get the time taken to travel from A to B.

Time = 720 / 90

Time = 8 hours

So, he is taking 8 hours to cover the distance 720 km. He started his travelling 8 hours before the 4 pm.

4 + 12 ==> 16 - 8 ==> 8 am

**Note :**

Time duration between 8 am to 3.12 pm is 7 hours 12 minutes. Converting the minutes into hours, dividing 12 by 60, we get 1/5. That is 0.2.

So it is 7.2 hours.

By applying it in (1), we find the speed.

7.12 = 720/Speed

Speed = 720/72

Speed = 100 km/hr

Hence the required speed is 100 km/hr.

- Find the time taken by the train to pass a man
- Find the time taken by a train to pass a bridge or tunnel
- Train passes a moving object in the same direction
- Problems on finding the length of the train
- Finding the average speed of the round trip
- Finding the speed when the distance traveled is same

After having gone through the stuff given above, we hope that the students would have understood how to find the time taken by a train to pass a man.

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