Answer:
Lucas's friend village is 45 miles away from his house.
Explanation:
Let the distance traveled from Lucas's home to friends village be 'd'.
Also Let the speed of the cycle be denoted by 's'.
Now given:
It takes Lucas 3 hours to cycle from his home to his friends village.
Time required to to cycle = 3 hours
Now we know that;
Distance is equal to speed times time.
framing in equation form we get;

Also Given:
if travels 5 mph slower, it will take him 1.5 hours longer.
Therefore speed =

Time required to cycle the friends village =

So equation for distance can be framed as;

Now By using Transitive Property of Equality which states that;
if

Hence from equation 1 and equation we can say that;

Now Combining the like terms we get;

Dividing both side by 1.5 we get;

Now we know the speed so we will find the distance.
Substituting the value of s in equation 1 we get;

Hence Lucas's friend village is 45 miles away from his house.