In this section, you 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.
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
So, 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
So, the required speed is 100 km/hr.
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