SOLUTION: Hello, I am working on a word problem that I need some assistance on. Here it is: A bus leaves a station at 1pm, traveling west at an average rate of 44m/h. One hour later a secon

Question 111994: Hello, I am working on a word problem that I need some assistance on.
Here it is: A bus leaves a station at 1pm, traveling west at an average rate of 44m/h. One hour later a second bus leaves the same station at, traveling east at a rate of 48m/h. At what time will the two buses be 274 miles apart?
Now what I have been trying to do is take the rate of 44m/h and 48m/h and divide that into 274. I have come close to 7pm for the time at which the two buses will be 274 mi. apart. Is this the correct way of solving this problem or am I off base here? I appreciate your help here.
Thank You, Barb Neely
Found 3 solutions by BrittanyM, ankor@dixie-net.com, jim_thompson5910:
Answer by BrittanyM(80)   (Show Source): You can put this solution on YOUR website!
The fisrt bus left at 1:00PM going at 44mph. The total distance that we are looking for is 274m. We need to subtract the 44M forom the total of 274M since the second bus doesn't start until an hour later. So now, our total distance is 230M.
274M - 44M = 230M
Now, we can find the combined rate at which the busses are separating.
44mph + 48mph = 92mph
We can plug are known variables into the distance formula to find T, time.
D = RT
230M = 92mphT
T = 2.5
Two and a half hours plus two o'clock (the time that the second bus started) gives us a time of 4:30PM.
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
A bus leaves a station at 1pm, traveling west at an average rate of 44m/h. One hour later a second bus leaves the same station at, traveling east at a rate of 48m/h. At what time will the two buses be 274 miles apart?
:
The best way to do this is just write an equation that adds the two distances to equal 274 mi:
;
Let t = travel time (in hrs) of the 1st bus to be 274 mi from the 2nd bus
Then
(t-1) = travel time of the 2nd bus to reach that 274 mi point
:
Distance = speed * time
:
2nd bus dist + 1st bus dist = 274
48(t-1) + 44t = 274
48t - 48 + 44t = 274
48t + 44t = 274 + 48
92t = 322
t = 322/92
t = 3.5 hrs
:
3.5 hrs after 1 pm = 4:30 the time they're 274 mi apart
:
:
WE can check this, the 2nd bus is traveling for only 2.5 hrs
48*2.5 = 120 mi from the starting point at 4:30 (leaves at 2pm)
44*3.5 = 154 mi from the starting point at 4:30 (left at 1 pm)
-------------
total mi:274 mi
:
Did this make sense to you?

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Let =distance bus #1 travels and =distance bus #2 travels

So we want to know when their distance apart is 274 miles. So this means

Now using the distance-rate-time equation, we get

Here r=44 mph

Since the 2nd bus starts 1 hour later, it's traveling time is 1 hour less. So t is really

Here r=48 mph

Distribute

Now go back to the first equation

Plug in and

Combine like terms on the left side

Add 48 to both sides

Combine like terms on the right side

Divide both sides by 92 to isolate t

Reduce

--------------------------------------------------------------
Answer:
So our answer is (which is approximately in decimal form)

So the first bus was on the road for 3.5 hours (which if added to 1:00 pm gets you 4:30 pm)

So at 4:30 pm the two buses are 274 miles apart
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