A car travels 100 mi at a certain speed. If the speed had been 5 mph​ faster, the trip would have been made in 1 hr less time. Find the speed.

Question

word problem. algebra one

Answer 1

Distance = (Rate)(Time), so Time = (Distance)/(Rate)

 

Let x = original speed

 

(Time traveled at faster speed) = (Time traveled at slower speed) - 1

 

So, 100/(x+5) = 100/x - 1

 

Multiply through by the LCD, x(x+5) to obtain:

 

   100x = 100(x+5) - x(x+5)

 

   100x = 100x + 500 - x² - 5x

 

   x² + 5x - 500 = 0

 

   (x+25)(x-20) = 0

 

So, x = -25 or x = 20

 

Since x can't be negative, x = 20 mph