SOLUTION: A bus is 13 miles from town traveling 80 miles an hour. A car leaves town at the same moment going the same direction as the bus at the same speed. The question is: After how lo

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Question 1033712: A bus is 13 miles from town traveling 80 miles an hour. A car leaves town at the same moment going the same direction as the bus at the same speed. The question is: After how long will the bus's distance from town be twice the car's distance? Thus far I have done the following:
x= hours bus and car travel
80x= distance car travels
13+80x=distance bus travels
I am having difficulty setting up the equation....for some reason I cannot "see" the solution. Thank you.
Found 3 solutions by josgarithmetic, addingup, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Try to draw a picture and form a data table. 
            rate     time        distance moved
BUS         80         t           d               80t=d
CAR         80         t           d               80t=d

t is used for both because this is the same time quantity.

Bus distance from the town becomes 80t+13.
Car distance from the town becomes 80t.
Review all of this a few times with concentration so you understand.


.
..
...
When that makes sense, look at the question.
How much time t for the bus to be twice the car, FROM THE TOWN?

80t%2B13=2%2880t%29
Again, review all of this including this equation so that it also makes sense for you.

You want to solve for t, in this last equation.
80t%2B13=2%2A80t
80t%2B13-80t=2%2A80t-80t
13=80t
13%2F80=t------this is fraction of an hour, so you can convert to minutes if you want.

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
b= bus
c= car
c = 80x
b = 13+80x
find b = 2c
`````````````````````````````````
13+80x = 2*80x
13+80x = 160x subtract 80x from both sides and flip the equation to get the unknown on the left side -it looks better:
80x = 13
x = 13/80 = 0.1625 hours; 0.1625*60 = 9.75 minutes = 9 minutes and 45 seconds
John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The bus is approaching the town and the car is
leaving the town
Let +d+ = distance in miles each one has traveled
Since they are traveling at the same rate, I can say
that the bus's distance from the town is +13+-+d+ and
the cars distance from town is +d+ at time +t+ in hours
-----------------------------------
The car's equation:
+d+=+80t+
The problem is telling me that:
+13+-+d+=+2d+
+3d+=+13+
+d+=+13%2F3+
----------------
+d+=+80t+
+13%2F3+=+80t+
+t+=+13%2F240++
In minutes:
+t+=+%28+13%2F240+%29%2A60+
+t+=+13%2F4+
+t+=+3.25+ min
After 3.25 min, the bus's distance from
town will be twice the car's distance
--------------------
check:
In +13%2F240+ hrs, the car travels
+d+=+80%2A%2813%2F240+%29+
+d+=+13%2F3+ mi
and the bus has traveled the same distance.
The bus is +13+-+13%2F3+=+%282%2F3%29%2A%2813%29+
miles from town
So, the bus is twice as far from town as the car
Hope you can follow this and hope I'm right