SOLUTION: When a car reduces its speed by 18 km/h, its wheels, 200 cm in circumference, take 1 second longer to make 50 revolutions. What was the car`s original speed ?
Question 665945: When a car reduces its speed by 18 km/h, its wheels, 200 cm in circumference, take 1 second longer to make 50 revolutions. What was the car`s original speed ? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! When a car reduces its speed by 18 km/h, its wheels, 200 cm in circumference, take 1 second longer to make 50 revolutions. What was the car`s original speed ?
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Find how far 50 rev is with a 200 cm circumference wheel, convert to meter = 100 meters
:
let s = original speed in meters/sec
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Find how many m/sec is 18 km/hr = 5 m/sec
then
(s-5) = the reduced speed in m/sec
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Write a time equation, time = dist/speed
: - = 1
multiply by s(s-5), resulting in
100s - 100(s-5) = s(s-5)
100s - 100s + 500 = s^2 - 5s
combine like terms, arrange as a quadratic equation
s^2 - 5s - 500 = 0
Factors to
(s-25)(s+20) = 0
The positive solution
s = 25 m/sec is the original speed
:
Convert to km/h = 90 km/hr
:
:
Check this, find the time required to travel 100 m at each speed
Reduced by 5 m/sec: 100/20 = 5 sec
Original speed: 100/25 = 4 sec, a 1 second difference
