SOLUTION: A car travels 600 km at an average speed of x km/h. If the car travels at a speed of (x-5) km/h, the journey would have taken 30 minutes longer. Form an equation in x and show tha

Algebra ->  Test -> SOLUTION: A car travels 600 km at an average speed of x km/h. If the car travels at a speed of (x-5) km/h, the journey would have taken 30 minutes longer. Form an equation in x and show tha      Log On


   

Question 1132154: A car travels 600 km at an average speed of x km/h. If the car travels at a speed of (x-5) km/h, the journey would have taken 30 minutes longer. Form an equation in x and show that it reduces to x2-5x=6000. Solve this equation and find the time taken when the car travels at a speed of x km/h.

x2 is x squared
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Thirty minutes is half-hour.
            SPEED         TIME        DISTANCE

As Done       x           600/x       600

If           x-5         600/(x-5)    600

Difference               1/2

The starting equation is 600%2F%28x-5%29-600%2Fx=1%2F2


STEPS:
1200%2F%28x-5%29-1200%2Fx=1
1200x-1200x%2B6000=x%5E2-5x
6000=x%5E2-5x
Simplification should give highlight_green%28x%5E2-5x-6000=0%29


Discriminant, 5%5E2%2B4%2A6000=24025=155%5E2

highlight_green%28x=%285%2B155%29%2F2%29
80 kilometers per hour