## Topic outline

• ### Distance

• Distance

Ria and Dia are two friends and both studies in the same school. Distance between Ria’s house and school is 1km whereas distance between Dia’s house and school is 1.5 km. This mean Ria’s house is closer to the school.

In above example, the word ‘Distance’ has been used. Now, what does the term ‘distance’ mean in mathematics?

Distance is the length of the space between two points. It is a numerical description of how far apart objects are.

In mathematics, distance is measured as

Distance = Speed x Time

Note: The unit of time in speed should be the same as that of the given time.

Illustration 1: How much distance will be covered in 3 hours at a speed of 70 per hour?

Solution:

Distance covered in 1 hour = 70 km

Distance covered in 3 hours = 70 x 3

= 210 km

Illustration 2: How much distance will be covered in 2 and half hour at a speed of 50 m per minute?

Solution:

2 and half hour = 60 + 60 + 30

= 150 min (1h=60min)

Distance covered in 1 minute = 50 m

Distance covered in 150 minutes

= 50 x 150 = 7500m

= 7500/1000 km

= 7.5 km

Illustration 3: A cyclist travels at a speed of 25 km/hour. How far will he travels in 30 minutes?

Solution:

1 hour = 60 min

Distance covered in 60 min = 25 km

Distance covered in 1 min = 25/60 km

Distance covered in 30 min

= 25/60 x 30

= 12.5 km

Illustration 4:  Arun drives his car at the speed of 25 meter per second. What is the distance covered in 1 hour?

Solution:

1 hour = 60 x 60 = 3600 seconds

Distance covered in 1 second = 25 m

Distance covered in 3600 seconds

= 25 x 3600

= 90000 m

= 90000/1000

= 90 km

Illustration 5:  Ravi jogs at 2 m per second. He jogs for 5 minutes. What is the distance covered by him.

Solution:

1 min = 60 seconds

5 minutes = 60 x 5 = 300 seconds

Distance covered in 1 second = 2 m

Distance covered in 300 seconds = 2 x 300

= 600 m

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