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# Two buses leave St. Louis from the same station....?

One leaves at 5:00 PM, traveling north to Chicago at an average speed of 50 mph. The second leaves at 5:30 PM, traveling south to New Orleans, also at an average speed of 50 mph. At what time are they 325 miles apart?
Member since:
May 12, 2006
Total points:
1,028 (Level 3)

Let Bus A = travelling to Chicago (north)
Let Bus B = travelling to New Orleans (south)

Given:
- Bus A left at 5:00pm and Bus B at 5:30pm
- Both Buses travel at 50mph

Solution:
- Find the distance (d) traveled by Bus A after 30 minutes (t).
= d = r*t
= d = 50mph * 0.5h
= d = 25miles ~~~~~ This is the distance between both buses upon Bus B's departure.

- Since both buses run at the speed, we can just split the remaining 300 miles (325-25)! So that would be 150miles per bus:
= d = r*t
= 150miles = 50mph * t
= 150miles / 50mph = t ~~~~~ divide both sides by 50
= 3hrs = t ~~~~~ This is the time needed by both bus to cover 150miles.

- add 3 hrs to 5:30pm:
= 5:30 + 3:00 = 8:30pm

FINAL ANSWER: At 8:30pm, the two buses will precisely be 325miles away from each other.
• 3 people rated this as good
good job!

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• Member since:
April 26, 2006
Total points:
4,325 (Level 4)
The first bus which left half an hour before the second one must have reached at least 25 miles away from St. Louis station. Now the leftover distance is 300 miles. Both the buses are travelling away from each other and at the same speed therefore after travelling for 150 miles more by each of them, the distance between them will be 150+150+25 = 325 miles. Hence the time taken to travel 150 miles is 3 hours at the speed given. Hence at 8 30 sharp both the buses will be 325 miles apart.
• by Tichy
Member since:
May 15, 2006
Total points:
1,518 (Level 3)
at 5:30 they are 25 miles apart, from then on they make 100 miles distance per hour. (325-25)/100 = 3, so the answer is 8:30 PM
• by hari m
Member since:
May 24, 2006
Total points:
141 (Level 1)
the first bus will travel 25 kms in north till 5:30 at 6:30 both will be 125 kms apart. at 8:30 they will be at 325 miles apart