SOLUTION: I submitted this problem quite a few days ago and did not get a response. I am resubmitting in hopes to get some help. Solve the following word problem. Be sure to show the equati

Question 72383: I submitted this problem quite a few days ago and did not get a response. I am resubmitting in hopes to get some help.
Solve the following word problem. Be sure to show the equation you use for the solution.
Science and medicine. A bus leaves a station at 1 P.M., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses be 274 mi apart?
This is what I have so far.
1st bus leaves=1pm travels west at 44 mi/h
2nd bus leaves=2pm travels east at 48 mi/h
274 miles apart

Found 2 solutions by bucky, jim_thompson5910:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The first bus travels from 1 p.m. to 2 p.m. at 44 mph. You can compute the distance that
this bus covers in that hour using the equation:
.
D = r*t
.
where D stands for distance, r is the rate or speed, and t is the amount of time. For this
bus the rate is 44 and the elapsed time is 1 hour. So the distance is:
.
D - 44*1 = 44 miles.
.
So the two buses are already 44 miles apart when the second bus departs at 2 p.m.
.
Since the buses are already 44 miles apart at 2 p.m. they only need to separate by 230 more
miles (274 miles - 44 miles = 230 miles).
.
Therefore, starting at 2 p.m. the distances that the two buses travel must add up to be
230 miles. You can use the distance equation for each bus, noting that their rates
are different. One bus has a rate of 44 mph and the other 48 mph. So their distances
are each given by D=r*t and they must add up to be 230 miles. For the first bus you have:
.
D = r*t = 44*t
.
and for the second bus you have:
.
D = r*t = 48*t
.
Add these two together and you get:
.
44t + 48t = 92t
.
(Notice that t is the same for each bus because it is time that started at 2 p.m. and
both buses are underway after that time. So the elapsed time after 2 p.m. is the same
for both buses.
.
To find the time it takes to cover the 230 miles of additional separation you set the
92t equal to 230 miles.
.
92t = 230
.
Divide both sides by 92 to solve for t and you get:
.
t = 230/92 = 2.5 hours or 2 hours and 30 minutes after 2 p.m.
.
and 2 hours and 30 minutes after 2 p.m. is 4:30 p.m. At that time they are separated
by the 230 miles plus the 44 mile head start the first bus had, so the total separation is
230 + 44 = 274 miles.
.
Hope this helps you to work your way through the problem.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Use the distance equation d=rt. You will have two distance equations
The first bus heading west.
The second bus heading east. (notice how the time is t-1. This is set up because for the first hour since the bus doesn't cover any distance). Now to find out how far each bus is away from each other, you simply add the two distances and . For instance, if one bus is 10 miles out and another is 5 miles out, then they are 10+5=15 miles away from each other.
Set up equation
Now solve for t

So it takes 3 and a half hours for the 2 buses to be 274 miles apart. To fully answer this question, 3 and a half hours after 1 PM is 4:30 PM.
Check:

If that doesn't help, you can plug t=3.5 into the first equation d=44t (the first bus). You'll see that the first bus traveled 154 miles. For the 2nd bus, instead of the bus travelling 3.5 hours, it travels 2.5 (since it starts an hour later). So thats why you must use t-1 instead of t for the second bus. When you plug in this info, you'll see that the 2nd bus travels 120 miles. If you add these 2 distances, you get 274 miles, which shows that our answer works. Hope this helps.
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