Smith bicycled 45 miles going east from Durango and Jones bi

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5mph more than Smith, and his trip took one-half hour longer that Smith\'s. how fast was each one traveling?

Solution

Smith DATA:
distance = 45 mi ; time = x hrs ; rate = d/t = 45/x mph
------------------------------------------------------------
Jones DATA:
distance = 70 mi ; time (x+0.5) hrs ; rate = d/t = 70/(x+(1/2)) = mph
-------------------------------------------------------------
Equation:
Jones\' rate - Smith\'s rate = 5
(45/x) - (70/((2x+1)/2) = 5
(9/x) - 28/(2x+1) = 1
9(2x+1) -28x = x(2x+1)
2x^2 + 30x = 18x+9
2x^2 + 12x - 9 = 0
x = [-12 +- sqrt(144 -4*2*-9)]/4
x = [-12 + 14.7]
x = 2.7 hrs
-----------------
Smith rate = 45/x = 45/2.7 = 16 2/3 mph
Jones rate = 16 2/3 + 5 = 21 2/3 mph