college algebra word problem please help

Question

Enrique went on a bike ride of 90 miles. He realized that if he had gone 25 mph faster, he would have arrived 15 hours sooner. How fast did he actually ride?

Enrique rode ____mph on his trip.

Answer 1

Usng D = RT, where T is thev time in hours & R is the original rate for traveling 90 miles, the second version would use rate = 25+R and time T-15; this gives us

90 = (R+25)(T-15)...second version of trip

90 = RT...first version of trip.  Therefore R = 90/T.

 

Substitute this in 2nd version, and you get a quadratic equation in variable T (you have to multiply by T to eliminate the denominators, thus getting a quadratic equation).

 

The answer will be T = 18 (the negative root is extraneous), so R = 5, i.e. 5 mi/hr originally.