Answer:
Lucas's friend village is 45 miles away from his house.
Step-by-step 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;
[tex]d =3s \ \ \ equation\ 1[/tex]
Also Given:
if travels 5 mph slower, it will take him 1.5 hours longer.
Therefore speed = [tex]s-5[/tex]
Time required to cycle the friends village = [tex]3+1.5 =4.5[/tex]
So equation for distance can be framed as;
[tex]d =4.5(s-5)\\\\d =4.5s-22.5 \ \ \ \ \ equation\ 2[/tex]
Now By using Transitive Property of Equality which states that;
if [tex]a=b \ \ and\ \ b = c \ \ \ so \ \ \ a=c[/tex]
Hence from equation 1 and equation we can say that;
[tex]3s=4.5s-22.5[/tex]
Now Combining the like terms we get;
[tex]4.5s-3s =22.5\\\\1.5s = 22.5[/tex]
Dividing both side by 1.5 we get;
[tex]\frac{1.5s}{1.5}=\frac{22.5}{1.5}\\\\s=15\ m/h[/tex]
Now we know the speed so we will find the distance.
Substituting the value of s in equation 1 we get;
[tex]d =3s =3\times15 =45 \ miles[/tex]
Hence Lucas's friend village is 45 miles away from his house.
