Answer:
[tex]Distance=45\ miles[/tex]
Step-by-step explanation:
[tex]Let\ distance\ between\ Lucas\ home\ to\ friends\ village=d\\\\Let\ speed\ of\ Lucas's\ cycle=v\\\\Time\ taken=3\ hours\\\\distance=velocity\times time\\\\d=v\times 3\\\\d=3v[/tex]
[tex]Now\ if\ speed\ is\ 5mph\ slower\ \Rightarrow\ speed=v-5\\\\Time\ taken=3+1.5=4.5\\\\distance=velocity\times time\\\\d=(v-5)\times 4.5=4.5v-22.5\\\\d=4.5v-22.5[/tex]
[tex]d=3v...................eq(1)\\\\d=4.5v-22.5.....eq(2)\\\\1.5\times eq(1)-eq(2)\\\\1.5d-d=1.4\times 3v-4.5v+22.5\\\\0.5d=4.5v-4.5v+22.5\\\\0.5d=22.5\\\\d=\frac{22.5}{0.5}\\\\d=45\ miles[/tex]
