SOLUTION: A bus left point for point y. Two hours later a car left x for y and arrived at y at the same time as the bus. If the car and the bus left simultaneously from the opposite ends x a

Question 887080: A bus left point for point y. Two hours later a car left x for y and arrived at y at the same time as the bus. If the car and the bus left simultaneously from the opposite ends x and y towards each other, they would meet 1.33 hours after the start. How much time for the bus to travel from x to y ?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bus left point for point y.
Two hours later a car left x for y and arrived at y at the same time as the bus.
If the car and the bus left simultaneously from the opposite ends x and y towards each other, they would meet 1.33 hours after the start.
How much time for the bus to travel from x to y ?
:
Choose a convenient value for the dist from x to y: 133 miles
Let b = the bus speed
let c - the car speed
then
133/b = the bus travel time\
133/c = the car travel time
:
"Two hours later a car left x for y and arrived at y at the same time as the bus."
therefore
bus time - 2 hrs = car time
- 2 =
mult equation by bc, resulting in:
133c - 2bc = 133b
c(133-2b) = 133b
c =
:
" If the car and the bus left simultaneously from the opposite ends x and y towards each other, they would meet 1.33 hours after the start. "
car dist + bus dist = 133 mi
1.33b + 1.33c = 133
simplify, divide by 1.33
b + c = 100
replace c with
b + = 100
multiply by (133-2b) to get rid of the denominator
b(133-2b) + 133b = 100(133-2b)
133b - 2b^2 + 133b = 13300 - 200b
combine like terms to form a quadratic equation
-2b^2 + 133b + 133b + 200b - 13300 = 0
-2b^2 + 466b - 13300 = 0
simplify divide by -2
b^2 - 233b + 6650 = 0
Using the quadratic formula I got two solutions
b = 199.7, not reasonable
and
b = 33.3 mph, as the bus speed
"How much time for the bus to travel from x to y ?"
133/33.3 = 4 hrs
:
:
Check this by finding the car speed, we know: b + c = 100
33.3 + c = 100
c ~ 66.7 mph is the car speed
Find the car time
133/66.7 ~ 2 hrs (started 2 hr later and arrive at the same time)

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