SOLUTION: A bus is travelling from point A to point B. The distance between the two points is 120 k"m. One day the bus stops exactly in the middle of the way for 10 minutes. To not be late b

Question 862634: A bus is travelling from point A to point B. The distance between the two points is 120 k"m. One day the bus stops exactly in the middle of the way for 10 minutes. To not be late by its schedule, the bus had to increase its speed by 12 to not be late. what was the buses initial speed?
Thank You
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A bus is traveling from point A to point B.
The distance between the two points is 120 k"m.
One day the bus stops exactly in the middle of the way for 10 minutes.
To not be late by its schedule, the bus had to increase its speed by 12 to not be late.
what was the buses initial speed?
:
let s = the initial speed
then
= required travel time
:
Change 10 min to 1/6 hr
:
the equation
1st 60km time + 10 min + 2nd 60km time = required time
+ + =
multiply by common denominator: 6s(s+12), cancel the denominators
6(s+12)(60) + s(s+12) + 6s(60) = 6(s+12)(120)
60(6s+72) + s^2 + 12s + 360s = 720(s+12)
360s + 4320 + s^2 12s + 360s = 720s + 8640
Combine like terms on the left to form a quadratic equation
s^2 + 360s + 12s + 360s - 720s + 4320 - 8640 = 0
s^2 + 12s - 4320 = 0
Factors to
(s+72)(s-60) = 0
the positive solution
s = 60 km/h is the initial sped
:
:
Check this by finding the time
120/60 = 2 hrs is the required time
then
+ + = 2
1 + + = 2
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