What is the distace travelled by the hero in km?

Question

The hero,Anti-mage covered a certain distamce at a certain speed.If he movved 3 kph faster,he would have taken 40 minutes less.Howecer if he had moved 2 kph slower,, he woukd take 40 minutes more.What is the distace travelled by the hero in km?

Answer 1

distance=speed × time.

Let x=required distance,  s=speed, t=time, so x=st. The distance x is fixed.

Also, x=(s+3)(t-⅔)=(s-2)(t+⅔)=st.

Therefore st-⅔s+3t-2=st+⅔s-2t-4/3. Note that the term st cancels out:

5t=4s/3+2/3, 15t=4s+2 so t=(4s+2)/15.

And: st-⅔s+3t-2=st, -2s+9t-6=0, t=(6+2s)/9.

We now have two expressions for t in terms of s, which can be equated:

(4s+2)/15=(6+2s)/9, multiply through by 45: 3(4s+2)=5(6+2s), 12s+6=30+10s, 2s=24, s=12 kph.

So t=(6+24)/9=30/9=10/3=3⅓hrs.

Therefore, x=12×3⅓=40km.

CHECK

s+3=15kph, s-2=10kph, t+40 mins=4hrs, t-40 mins=2hrs 40 mins (2⅔hrs).

x=40=15×8/3=10×4.