Sean drove at a uniform speed of 90km/h. He started driving at 5:30 am and
reached his destination at 1.30 pm. Mary started driving at the same time as
Sean and reaches the same destination in 6 hrs. How far was Sean from his
destination when he was 150 km apart from Mary?
Sean drove From 5:30 AM till 1:30 PM, so he drove for 8 hours.
Since Sean drove for 8 hours at 90 km/h, that means that the distance to the
destination was 90∙8 = 720 km.
Mary drove for 6 hours from 5:30 AM and got to the same place at 11:30 AM.
So her speed was 720/6 = 120 km/h
So their rate of separation was the difference in their speeds.
So they separated at 120-90=30 km/h
Let's find the time at when they were 150 km apart (when they had separated
by 150 km):
time = (separation distance)/(separation rate) = 150/30 = 5 hours
So Sean had driven 5 hours when he was 150 km behind Mary.
Since Sean's rate was 90 km/h, he had driven 90∙5 = 450 km.
Since the distance to the destination was 720 km, Sean was 720-450=270 km
from his destination.
Answer: Sean was 270 km from his destination when he was 150 km apart from
Mary
------------------
Analysis: Sean was the slower driver. They left at 5:30. Their destination
was 720 km away. 5 hours later at 10:30 AM, Sean was 450 km from the
starting point and 270 km from the destination. They were 150 km apart,
Mary was 600 km from the starting point and 120 km from the destination.
Mary arrived at the destination at 11:30, and Sean arrived 2 hours later at
1:30 PM.
Edwin
Sean drove at a uniform speed of 90km/h. He started driving at 5:30 am and
reached his destination at 1.30 pm. Mary started driving at the same time as
Sean and reaches the same destination in 6 hrs. How far was Sean from his
destination when he was 150 km apart from Mary?
Sean traveled a total of 8 hrs (5:30 am - 1:30 pm), and at 90 km/h, destination-distance was: 8(90), or 720 km
With Mary taking 6 hours to complete trip, her speed was:
You must realize that Mary's rate was faster than Sean's (120 km/h to 90 km/h), which means that she was ahead of him after they left the same location
at the same time and were heading to the same destination
Let the distance Mary was, from the destination be x
Then Sean was 150 + x from destination when Mary was 150 km in front of him
When Sean was 150 km from Mary, he'd traveled 570 - x from the starting point, in hours
When Mary was 150 km IN FRONT of Sean, she'd traveled 570 - x + 150 from the starting point, in hours
With both leaving the same location at the sane time, they reached their respective distances at the sane time.
We then get the following TIME equation:
4(570 - x) = 2,160 - 3x ------ Multiplying by LCD, 360
2,280 - 4x = 2,160 - 3x
- x = - 120 ====>
Therefore, when Mary was 150 km in front of Sean, Sean was 150 + 120, or from the destination.