__Solution 5__The distance between Town Y and Town Z is 7 km .

At the beginning , both Ali and Bob are at Town Y .

Ali walked from Town Y to Town Z at a constant speed .

After Ali had walked for 1 km , Bob discovered that Ali had left his belongs at Town Y .

Bob immediately ran after Ali at a constant speed of 4 km/h .

After handing over the belongings to Ali , Bob turned back and started running towards Town Y at the same speed .

**(Draws a line representing distance between Y , Z and X*)**

**Since both Bob and Ali reached Y and Z respectively at the same time ,**

Time taken for Bob from Y to X =

Time taken for Bob from X to Y =

Time taken for Ali from 1 km point to X =

Time taken for Ali from X to Z

Time taken for Bob from Y to X =

Time taken for Bob from X to Y =

Time taken for Ali from 1 km point to X =

Time taken for Ali from X to Z

**(All the time taken are the same*)**

**Since time taken for Ali from 1 km point to X = Time taken for Ali from X to Z ,**

**we can conclude that x km = y km = (7-1) / 2 = 3 km**

Bob from X to Y :

Distance = Speed x Time

( 3 + 1 ) km = 4 km/h x Time

Time = 1 hour

Ali from X to Z :

Distance = Speed x Time

3 km = Speed x 1 hour

Speed = 3 km/h

Ali's speed was 3 km/h .

Bob from X to Y :

Distance = Speed x Time

( 3 + 1 ) km = 4 km/h x Time

Time = 1 hour

Ali from X to Z :

Distance = Speed x Time

3 km = Speed x 1 hour

Speed = 3 km/h

Ali's speed was 3 km/h .

__Solution 6__Ali, Bob, Cid travel from Town Y to Town Z in a straight road .

They leave Town Y at the same time and travel at constant speed towards Town Z .

Ali drives a car at speed of 56 km/h .

Bob jogs at a speed of 8 km/h .

Cid walks at a speed of 7 km/h .

At the start , Ali gives a lift to Bob from Town Y and drops Bob somewhere along the road to Town Z before returning to pickn up Cid and travel to Town Z .

All three of them arrived at Town Z at the same time .

If Bob had jogged for 2.8km , how far did Cid walk ?

**(This question can be confusing, so it's important to draw a line to see clearly distance traveled by each of the 3 persons*)**

**(Ignore the vertical lines for Path by Ali*)**

(D is the point where Ali drops Bob off and C is the point where Ali picks up Cid*)

(D is the point where Ali drops Bob off and C is the point where Ali picks up Cid*)

**Bob:**

**Distance = Speed x Time**

**2.8 km = 7 km/h x Time (2.8 km is the distance from D to B)**

**Time = 0.4 hr**

**Time taken for Bob to travel from D to B = Time taken from Ali to travel from D to C to B**

**Ali:**

**Distance = Speed x Time**

**Distance = Speed x Time**

**D-to-C + C-to-D + D-to-B = 56 km/h x 0.4 hr**

**2 x ( C-to-D ) + 2.8 km = 22.4 km ( D-to-B is 2.8 km and D-to-C is equal to C-to-D )**

**C-to-D = 9.8 km**

**Distance = Speed x Time**

**Time = Distance / Speed**

**Time taken for Ali to travel from A to C to D to C = Time taken for Cid to travel from A to C**

**(A-to-C + 9.8 km + 9.8 km ) x (7) = (A-to-C) x (56)**

**7 x (A-to-C) + 137.2 = 56 x (A-to-C)**

**49 x (A-to-C) = 137.2**

**A-to-C = 2.8 km**

**Cid walked 2.8km .**