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In 6 hours Harka walks 6 km more that Dorje walks in 3 hours. In 8 hours Dorje walks 12 km more than Harka walks in 9 hours. Find their speed in km per hour.

Let Vh = Harka’a speed

Let Vd = Dorje’s speed.

In 3 hrs, Dorke walks S1 = 3Vd km

In 6 hrs, Harka walks s2 = 6Vh km

And s2 = s1 + 6

6Vh = 3Vd + 6

In 8 hrs, Dorke walks S3 = 8Vd km

In 9 hrs, Harka walks s4 = 9Vh km

And s3 = s4 + 12

8Vd = 9Vh + 12

Our simultaneous equations now are,

6Vh - 3Vd = 6     -------------------- (1)

8Vd - 9Vh = 12    ------------------- (2)

Multiply (1) by 3, and (2) by 2,

18Vh - 9Vd = 18     ----------------- (3)

16Vd - 18Vh = 24    ---------------- (4)

Add (4) and (3)

7Vd = 42

Vd = 6 km/hr

Using (1),

6Vh - 18 = 6

6Vh = 24

Vh = 4 km/hr

Harka’s speed is: 4 km/hr   Dorje’s speed is: 6 km/hr

by Level 11 User (81.5k points)

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