## FINDING THE SPEED WHEN THE DISTANCE TRAVELED IS SAME

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.

## Related topics

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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