Question

It takes me 8 hrs to reach city A from B, if i increase my speed by 6 km hr it takes me 1 hr 20 min less. Find the distance between the two cities.

Answer 1

Let the original speed be s, and distance between A and B is d.

s = d/8.....(1)

For 2nd case, we have

s + 6 = d / (6 hr 40 min)

6 hr 40 min = 6 2/3 hr or 20/3 hr

s + 6 = d / (20/3)

s + 6 = 3d / 20....(2)

Putting (1) in (2)

d/8 + 6 = 3d/20

5d/40 + 240/40 = 6d/40

d/40 = 240/40

d = 240

Distance between A and B is 240 km

Answer 2

Hello Dear.

Here is the answer---

Let the distance between the Cities A and B is x km.

In First Case,
Distance = x km.
Original Time = 8 hrs.

∵ Speed = Distance/Time
∴ Speed = x/8 km/hr.

Now, In Second Case,

Speed = Original Speed + 6 km/hr.
     = x/8 + 6
    = (x + 48)/8 km/hr.


1 hrs + 20 min. = 60 min. + 20 min.
 = 80 min.
 = 80/60 hrs.
 = 4/3 hrs.

Now,

Time = Original Time - 1 hrs + 20 min.
         = 8 hrs. -  4/3 hrs.
         = (24 - 4)/3 hrs.
         = 20/3 hrs.

∵ Speed = Distance/Time
∴ (x + 48)/8 = x/(20/3)
⇒ $\frac{x + 48}{8} = \frac{3x}{20}$
⇒ 20 × (x + 48) = 8 × 3x 
⇒ 20x + 960 = 24x
⇒ 4x = 960
⇒ x = 240 km.


∴ Distance between the two cities is 240 km.


Hope it helps.