SOLUTION: A car travels 20km / h faster than a cyclist. The car takes one hour less than the cyclist to travel 150 km. Assuming the speed of the car is x km/h a) write down in terms of x e

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Question 941218: A car travels 20km / h faster than a cyclist. The car takes one hour less than the cyclist to travel 150 km. Assuming the speed of the car is x km/h
a) write down in terms of x expressions for the time takrn by the car and the cyclist
B) form a quadratic equation to connect these times
C) SOLVE the equation to find the speed of the car and the cyclist
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A car travels 20km / h faster than a cyclist.
The car takes one hour less than the cyclist to travel 150 km.
Assuming the speed of the car is x km/h
a) write down in terms of x expressions for the time taken by the car and the cyclist
Car time: 150%2Fx; Cyclist: 150%2F%28%28x-20%29%29
:
B) form a quadratic equation to connect these times
Cyclist time - car time = 1 hr
150%2F%28%28x-20%29%29 - 150%2Fx = 1
multiply equation by x(x-20)
x(x-20)*150%2F%28%28x-20%29%29 - x(x-20)*150%2Fx = x(x-20)
Cancel the denominators and we have
150x - 150(x-20) = x^2 - 20x
150x - 150x + 3000 = x^2 - 20x
combine to form a quadratic equation on right
f(x) = x^2 - 20x - 3000
:
C) SOLVE the equation to find the speed of the car and the cyclist
x^2 - 20x - 3000 = 0
Use the quadratic formula; a=1; b=-20; c=-3000
I got a positive rounded off solution of:
x = 65.68 is speed of the car
and
45.68 km/hr is the speed of the cyclist (20 km/hr less)
:
Check this by finding the actual time of each
Cyclist: 150/45.68 = 3.28 hrs
Car: 150/65.68 = 2.28 hrs,