Question

2. A man takes 10 hours to go to a place and come back by walking both the ways. He
could have gained 2 hours by riding both the ways. The distance covered in the
whole journey is 18 Km. Find the average speed for the whole journey if he goes by
walking and comes back by riding.

Answer 1

Given:

A man take 10 hours to go and com back by walking.

He gains 2 hours by riding both ways.

The journey is 18 km.

To Find:

The average speed if he goes by walking and comes back by riding.

Solution

Find the time needed to walk there:

Time needed to walk there = 10 ÷ 2

Time needed to walk there = 5 hours

Find the time needed to ride back:

Time needed to ride back = (10 - 2) ÷ 2

Time needed to ride back = 4 hours

Find the total time:

Total time = 5 + 4

Total time = 9 hours

Find the average speed:

Average speed = Total distance ÷ Total Time

Average speed = 18 ÷ 9

Average speed = 2 km/h

Answer: The average speed is 2 km/h

Answer 2

Given :

Time taken while walking both the way = t = 10 hours

The time taken by riding both the way = T = 10 - 2 = 8 hours

Total distance to cover = 18 km

To Find :

The average speed for the whole journey if he goes by  walking and comes back by riding

Solution :

Let the average speed of walking = w km/h

The average speed of riding = r km/h

∵  For riding

Speed = $\dfrac{18 km}{8 hours}$

          = 2.25 km/h

For walking

Speed =   $\dfrac{18 km}{10 hours}$

            = 1.8 km/h

Now,

Average speed = $\dfrac{Total speed}{2}$

                          = $\dfrac{2.25 km/h+1.8 km/h}{2}$

                          = $\dfrac{4.05}{2}$

                          = 2.025 km/h

Hence,  the average speed for the whole journey if he goes by walking and comes back by riding is 2.025 km/h  Answer