Answer:
12 km/h
Step-by-step explanation:
The formula for speed is distance divided by time
S=D/T
T=D/S
Let the rate for the first 18 km of his trip be x km/h
Time taken in this first phase of the trip = 18/ x hrs
Then the rate for the remaining 6 km of his trip will be x-6 km/h
Time taken in this second phase of the trip is : 6/ x-6 hrs
Equation for the entire trip is;
18/x + 6/x-6 = 1.5
multiply each term by the common divisor x(x-6)
x(x-6)*18/x + x(x-6)* 6/x-6= 1.5* x(x-6)
18(x-6) +6 x =1.5 (x²+6 x)
18 x -108 +6 x = 1.5 x² - 9 x
24 x -108 = 1.5 x² -9 x
1.5 x² -33 x + 108 = 0 --------divide each term by 1.5
x²-22 x + 72 = 0 --------solve the quadratic equation
x²-4 x -18 x + 72 =0
x(x-4) -18 (x-4) =0
(x-18) (x-4) =0
x-18 =0
x= 18 or
x-4 =0
x=4
The rate in the 6 km will be
x-6 = 18-6 = 12 km/h