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 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,

$s=\frac{x}{3}-5$

Time taken in the second instance when travelling at a slower speed

=$\frac{x}{\frac{x}{3}-5 }=4.5\\ \\\frac{3x}{x-15} =4.5\\\\\\3x=4.5(x-15)\\\\3x=4.5x-67.5\\\\\\67.5=4.5x-3x\\\\\\67.5=1.5x\\\\\\67.5/1.5=x\\\\\\45=x$

The distance from friend's village to Lucas's house is 45 miles

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Formula for speed:brainly.com/question/13664094

Keywords: cycle,home, village, travels,slower,longer

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