NONE CAN SOLVE! It takes Lucas 3 hours to cycle from his home to his friend's village. But if he travels 5 mph slower, it will take him 1.5 hours longer. How far is the friend's village from Lucas' house?

45 miles

It takes Lucas 3 hours to cycle from his home to his friend's village:

3 hours • (a certain speed) = distance in miles

If he travels 5mph slower, it will take him 1.5 hours longer:

4.5 hours • (the same speed - 5mph) = the same distance in miles

Equation:

4.5 • (x - 5) = 3x

4.5x - 22.5 = 3x

1.5x = 22.5

x (speed) = 15mph

Distance between Lucas' house and his friend's village:

3hours • 15mph = 45 miles

OR

4.5hours • (15mph - 5mph) = 45 miles