SOLUTION: The driving distance between Pensacola and Key West is 792 miles. Bus A leaves Pensacola at 6:00 a.m. traveling at an average 42 miles per hour. Bus B leaves Key West at 7:00 a.m.

Algebra ->  Real-numbers -> SOLUTION: The driving distance between Pensacola and Key West is 792 miles. Bus A leaves Pensacola at 6:00 a.m. traveling at an average 42 miles per hour. Bus B leaves Key West at 7:00 a.m.       Log On


   

Question 551051: The driving distance between Pensacola and Key West is 792 miles. Bus A leaves Pensacola at 6:00 a.m. traveling at an average 42 miles per hour. Bus B leaves Key West at 7:00 a.m. traveling at an average speed of 33 miles per hour. At what distance, in miles, from Key West will the two buses meet?
This question has me confused so please help me with this.
Found 2 solutions by oberobic, mananth:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The buses are converging at their combined speed: 42+33 = 75 miles/hr.
When they meet, they will have covered the entire distance: 792 miles.
The fundamental distance equation is: d = r*t
We know 'd' and 'r', so we can solve for 't'.
t = 792 miles / 75 miles/hr = 10.56 hr.
.56 hr * 60 min/hr = 33.6 min.
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We now have to arrange these facts to answer the question: How far from Key West will they be?
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Well, the bus that left Key West was going 42 mph * 10.56 hr = 443.52 miles.
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We can check the distance based on leaving Pensacola.
That bus traveled 33 mph * 10.56 hr = 348.48.
That is how far from Pensacola they are. We know the distance from Pensacola to Key West is 792,
so the bus is 792 - 348.48 = 443.52.
That's confirms the answer since it matches the other distance.
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Answer: The buses are 443.52 miles from Key West when they meet.
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Done.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Pensacola at 6:00 a.m. traveling at an average 42 miles per hour. Bus B leaves Key West at 7:00 a.m. traveling at an average speed of 33 miles per hour. At what distance, in miles, from Key West will the two buses meet?
This question has me confused so please help me with this.
Bus I = 42 mph
Bus II = 33mph
Bus I has left 1 hour early
Bus I has traveled 42 miles before Bus II starts
The buses are travelling in opposite directions
so their combined speed = 75 mph
Balance distance = 792-42=750 miles
t=d/r
d=750
r=75
t=750/75
t=10 hours after Bus II starts at 7.00 am
From key west Bus II has traveled 33* 10 =330 miles
From Pensacola Bus I has traveled 11*42= 462 miles ( it left 1 hour early)
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