The distance from friend's village to Lucas's house is 45 miles
Step-by-step explanation:
Lets assume the distance from Lucas home to friend's village is x miles
The time taken to cycle from Lucas home to friend's village is 3 hrs....t₁
The time taken if travelling at a 5 mph reduced speed is 1.5 hrs longer......t₂
t₂=4.5 hrs
t₁= 3 hrs
Speed for cycle in first instance, where t₁=3 hrs and distance is x miles
s₁=d/t = x/3 mph
Speed for cycle if travelling at a slower speed,
[tex]s=\frac{x}{3}-5[/tex]
Time taken in the second instance when travelling at a slower speed
=[tex]\frac{x}{\frac{x}{3}-5 }=4.5\\ \\\frac{3x}{x-15} =4.5\\\\\\3x=4.5(x-15)\\\\3x=4.5x-67.5\\\\\\67.5=4.5x-3x\\\\\\67.5=1.5x\\\\\\67.5/1.5=x\\\\\\45=x[/tex]
The distance from friend's village to Lucas's house is 45 miles
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Formula for speed:https://brainly.com/question/13664094
Keywords: cycle,home, village, travels,slower,longer
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