SOLUTION: plz help me find this answer.
A car travels a 750 km journey at an average speed of x km/h. If it had increased its speed by 18 km/h, the journey would have been 125 minutes sho
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A car travels a 750 km journey at an average speed of x km/h. If it had increased its speed by 18 km/h, the journey would have been 125 minutes sho
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Question 205644: plz help me find this answer.
A car travels a 750 km journey at an average speed of x km/h. If it had increased its speed by 18 km/h, the journey would have been 125 minutes shorter. Form an equation in x and show that it reduces to x²+ 18x= 6480. Solve this equation to find the value of x. Hence find the time taken when the car travels at x km/h. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A car travels a 750 km journey at an average speed of x km/h. If it had increased its speed by 18 km/h, the journey would have been 125 minutes shorter. Form an equation in x and show that it reduces to x²+ 18x= 6480. Solve this equation to find the value of x. Hence find the time taken when the car travels at x km/h.
:
x = actual speed
then
(x+18) = faster speed
:
Write a time equation; time =
:
Actual time = faster time + 125 min = +
multiply equation by 60x(x+18)
60x(x+18)* = 60x(x+18)* + 60x(x+18)*
Cancel the denominator, results
60(x+18)*750 = 60x*750 + x(x+18)*125
:
45000(x+18) = 45000x + 125x(x+18)
:
45000x + 810000 = 45000x + 125x^2 + 2250x
:
Arrange as a quadratic equation on the right
0 = 125x^2 + 2250x + 45000 - 45000 - 810000
0 = 125x^2 + 2250x - 810000
:
Simplify, divide by 125
x^2 + 18x - 6480 = 0; the given equation
:
Solve for x by factoring the equation (or you can use the quadratic formula)
(x-72)(x+90) = 0
Positive solution is what we want here:
x = 72 km/hr
;
:
Is this true? find the time of each using decimals
750/72 = 10.4
750/90 = 8.3 (18km/hr faster)
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differ = 2.1 hrs which is 126 min ~ 125 min
