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Algebra Level 1

There is a straight highway across a jungle. On that highway, there are four villages located at different distances apart. The third village was 60 km far from the first village; the fourth village was 40 km far from the second village and the third village was 10 km nearer to the fourth village than it was to the second village. How far is the fourth village from the first village?

64 km 59 km 75 km 57 km

Kanika Kachhwaha by Kanika Kachhwaha , 20, India

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2 solutions

Paulo Martins
Dec 1, 2014

Distance between 1st and 2nd village => x

Distance between 2nd and 3rd village => y

Distance between 3rd and 4th village =>z

Distance between 1st and 3rd => x + y = 60

Distance between 2nd and 4th => y + z = 40

Distance between 2nd and 3rd => y = 10 + z or y - z = 10

Distance between 1st and 4th => x + y + z

y+z=40

y-z=10

then 2y=50 => y=25

x+y=60 then x+25=60 => x=35

y+z=40 then 25+z=40 => z=15

x+y+z=35+25+15=75

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Kanika Kachhwaha
Jun 12, 2014

Distance between second and fourth village = 40 km ⇒ Distance between second and third village + Distance between third and fourth village = 40 km ⇒ Distance between second and third village + (Distance between second and third village – 10) = 40 km ⇒ 2 × Distance between second and third village = 50 km ⇒ Distance between second and third village = 25 km So, distance between third and fourth village = 15 km

Thus, distance between the first and the fourth village = 60 + 15 = 75 km

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