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

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)   (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?

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.

------this is fraction of an hour, so you can convert to minutes if you want.
Answer by addingup(3677)   (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)   (Show Source): You can put this solution on YOUR website!
The bus is approaching the town and the car is
leaving the town
Let = 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 and
the cars distance from town is at time in hours
-----------------------------------
The car's equation:

The problem is telling me that:

----------------

In minutes:

min
After 3.25 min, the bus's distance from
town will be twice the car's distance
--------------------
check:
In hrs, the car travels

mi
and the bus has traveled the same distance.
The bus is
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
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