Question

It takes Lucas 3 hours to cycle from his home to his friends village but if travels 5 mph slower, it will take him 1.5 hours longer. How far is the friends village from Lucas's house

Answer 1

The answer is 45 miles from his house

Answer 2

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;

`d =3s \ \ \ equation\ 1`

Also Given:

if travels 5 mph slower, it will take him 1.5 hours longer.

Therefore speed =
`s-5`

Time required to cycle the friends village =
`3+1.5 =4.5`

So equation for distance can be framed as;

`d =4.5(s-5)\\\\d =4.5s-22.5 \ \ \ \ \ equation\ 2`

Now By using Transitive Property of Equality which states that;

if
`a=b \ \ and\ \ b = c \ \ \ so \ \ \ a=c`

Hence from equation 1 and equation we can say that;

`3s=4.5s-22.5`

Now Combining the like terms we get;

`4.5s-3s =22.5\\\\1.5s = 22.5`

Dividing both side by 1.5 we get;

`(1.5s)/(1.5)=(22.5)/(1.5)\\\\s=15\ m/h`

Now we know the speed so we will find the distance.

Substituting the value of s in equation 1 we get;

`d =3s =3*15 =45 \ miles`

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