Alexander B. answered • 09/14/15

PhD in Engineering with 20 yrs of Math and Science Teaching Experience

Hello Alex,

First, let's write the following system of linear equations pertinent to the problem, where

90/x = (90/y) -1

y=x-24

Next in the first equation re-written as:

90y=90x-xy

Substitute

y=x-24

Resulting in

90(x-24)=90x - x(x-24)

90x-2160 = 90x - x

The following Quadratic equation in its canonical form (you can solve it using online Quadratic Equation Solver: http://examn8.com/QuadraticEquations.aspx)

x

has only one positive solution:

**x**and**y**stand for the speed (km/h) of the faster and slower cars, correspondingly.90/x = (90/y) -1

y=x-24

Next in the first equation re-written as:

90y=90x-xy

Substitute

y=x-24

Resulting in

90(x-24)=90x - x(x-24)

90x-2160 = 90x - x

^{2}+24xThe following Quadratic equation in its canonical form (you can solve it using online Quadratic Equation Solver: http://examn8.com/QuadraticEquations.aspx)

x

^{2}-24x-2160=0has only one positive solution:

**x=60**(the second one is a negative value, which does not apply to this problem). Therefore the speed of the faster car is**60 km/h**and the speed of the slower car is correspondingly: y=60-24=**36km/h**Quick check: the travel time of the faster car is: 90/60 = 1.5hr, the travel time of the slower car is 90/36=2.5hr.

Hope this may help.

Hope this may help.

Alex A.

09/28/15