Problem Solving

Anurag@Gurome wrote:

goyalsau wrote:A person starts from hill top A, goes downhill, then along a plain and finally climbs to hill top B. He takes a total of 4 hours for the jouney travelling downhill @72kmph, on plains @63kmph and uphill @56kmph. However while returning back, from B to A, he takes 4 hours 40 mins with speeds being same. Find distance AB.

Referring to the above image, from A to B, the end of downhill and start of plains is C and end of plains and start of uphill is D.

Say, AC = x km, CD = y km and DB = z km
Thus, distance AB = (x + y + z) km

Therefore while going from A to B,

• Total time taken = (x/72) + (y/63) + (z/56) = 4
  => (7x + 8y + 9z) = 4*7*8*9 ........................................ (i)

And while going from B to A,

• Total time taken = (z/72) + (y/63) + (x/56) = (4 + 2/3)
  => (9x + 8y + 7z) = (4 + 2/3)*7*8*9 ........................................ (ii)

Add (i) and (ii) : (16x + 16y + 16z) = (4 + 4 + 2/3)*7*8*9 = (26/3)*7*8*9
=> (x + y + z) = (26*7*8*9)/(3*16) = (13*7*3) = 273

Therefore the distance AB is 273 km.

Anurag@Gurome wrote:

goyalsau wrote:I was not able to calculate values for x , y and z.

x + z = 168 , and y = 105 , But what about the individual vales of x and z,

Can we calculate that??????????

No, as we have two equations in three unknowns.