It takes Joey the postman 1 hours to run a 3 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?

a 11
b 12
c 13
d 14
e 15

Answer given is 12

But it should be 15 and here is my reasoning-

let his speed for first half of the journey be 3 miles an hour

let the return journey (2nd half) be x miles an hour
now,

avg speed =5 mile an hour

we know if the Av speed = $\frac{2*x1 *x2}{x1+x2}$ (Where X1 = speed m/hr in first half and X2 = speed in 2nd half)

(Plz Note - This formula only hold valid if both forward and return journey covered equal distance as in this case)

therefore $\frac{2*3*x}{3+x}$=5

Solving for X we get x=15 m/hr