### Question 1.

If some distance is traveled at a speed of ‘x’ km/h and the same distance is traveled at a speed of ‘y’ km/h. Then, the average speed during the whole journey:

**If the distance between Goa to Delhi is 750 km. A person goes at a speed of 60 km/h and returns at a speed of 40 km/h. Find the average speed.**__Example:____Solution:__### Question 2.

If the distance is different than average speed is:

**If the speed of the bus is 30 km/h for the 90 km and 35 km/h for the distance of 70 km. Find the average distance.**__Example:____Solution:__
If the speed ratio between P and Q is a:b, so to cover the same distance the ratio between times taken by them will be

**The ratio between the speed of two cars is 6:8. If the second car covers a certain distance in 9 hours, then find the time taken by the first car to cover the same distance.**__Example:____Solution:__### Question 4.

To find the time of halts when the speed with stoppages is

a km/h and speed without stoppages b km/h:

a km/h and speed without stoppages b km/h:

**A man running on a road without any stoppage at an average speed of 100 km /hr, and he covers the same distance with stoppage at an average speed of 80 km/hr. How many minutes per hour does boy stop?**__Example:____Solution:__### Question 5.

A man walks at x/y speed of his actual speed reaches his destination z mint later. To cover this distance actual time is:

Solution:

**Walking at 3/4th of usual speed, A person is late by 10 minutes. Find the usual time.**__Example:__Solution:

### Question 6.

A man walks at x/y speed of his actual speed reaches his destination z mint early. To cover this distance actual time is:

**Walking at 6/5th of usual speed, A person reached early by 5 minutes. Find the usual time.**__Example:____Solution:__### Question 7.

A & B start moving towards each other at same time. After meeting each other, they reach their destinations after ‘a’ and ‘b’ hrs respectively.

A’s Speed: B’s Speed = √b: √a

A:B = √b : √a

A:B = √9 : √4

A:B = 3:2

A’s Speed: B’s Speed = √b: √a

**Two trains, one from Delhi to Pune and the other from Pune to Delhi, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What will be the ratio of their speeds?**__Example:____Solution:__A:B = √b : √a

A:B = √9 : √4

A:B = 3:2

### Question 8.

A man/train leaves from A at x1 AM and reaches Q at x2 AM. Another man/train leaves from Q at y1 AM and reaches P at y2 PM. They will meet:

**A train leaves from Bombay at 6:30 AM and reaches Jaipur at 10:30 AM. Another train leaves from Jaipur at 9 AM and reaches Delhi at 12:30 PM. When they will meet?**__Example:____Solution:__
If the distance between A to B is D km. Two persons P and Q travel from points A to B, with the speed of 'a' and 'b' respectively and Q reaches B first, returns immediately and meets P at X, then

Distance traveled by P (from points A to X) =

Distance traveled by P (from points A to X) =

**Suhail and Meetu travel from point A to B, a distance of 48 km, at 7 km/ h and 9 km/ h, respectively. Meetu reaches B first and returns immediately and meets Suhail at R. Find the distance from points A to R.**__Example:____Solution:__### Question 10.

Relative Speed:

(i). If two objects are moving in the same direction with the speeds of a km/h and b km/h then their relative speed is |a‐b|.

(ii). If two objects are moving in opposite direction with the speeds of a km/h and b km/h then their relative speed is (a+b).

(i) If they walk in the same direction.

(ii) If they walk in opposite direction.

(i): Relative speed = Ia-bI

= I 4-5 I

= 1 km/h

(i). If two objects are moving in the same direction with the speeds of a km/h and b km/h then their relative speed is |a‐b|.

(ii). If two objects are moving in opposite direction with the speeds of a km/h and b km/h then their relative speed is (a+b).

**2 men A and B started from a place P walking at 4 km/h and 3 km/h respectively. How many km will they be a part at the end of 1 hour?**__Example:__(i) If they walk in the same direction.

(ii) If they walk in opposite direction.

Solution:Solution:

(i): Relative speed = Ia-bI

= I 4-5 I

= 1 km/h

(ii): Relative speed = a+b

= 4+5

= 9 km/h

= 4+5

= 9 km/h