Problems on Calculating Distance

Here we will learn to solve different types of problems on calculating distance.

We know, the formula to find out distance = speed × time


Word problems on calculating distance:

1. A train moves at a speed of 80 km/hr. How far will it travel in 36 minutes?

Solution:            

Using the unitary method;

In 60 minutes, distance covered = 80 km

In 1 minute, distance covered = 80/60 km

Speed = 80 km/hr

Time = 36 minutes or 36/60 hours

We know, formula of distance = speed × time

                                        = 80 × 36/60

                                        = 48 km

Therefore, the train will travel 48 km in 36 minutes.


2. A student goes to school at the rate of 7 ½ km/hr and reaches 10 minutes late. If he travels at the speed of 10 km/hr he is 10 minutes early. What is the distance to the school?

Solution:            

Let the distance to school be 1 km, then time taken to cover 1 km at the rate of 7 1/2 km/hr

= Distance /speed = 1/(15/2) = 2/15 hr = 2/15 × 60 minutes = 8 minutes

Time taken to cover 1 km at the rate of 10 km/hr         

= Distance /speed = 1/10 hr = 1/10 × 60 minutes = 6 minutes

Therefore, difference in time taken = (8 – 6) minutes = 2 minutes

But actual difference in time is 20 minutes

When the difference in time is 2 minutes, distance to school = 1 km

When the difference in time is 1 minute, distance to school = 1/2 km

When the difference in time is 20 minutes, distance to school = 1/2 × 20 km

Therefore, the distance to school is 10 km.


3. Two persons jog and covers the same distance at the speed of 6 km/hr and 4 km/hr. Find the distance covered by each one of them when one takes 10 minutes longer than the other.

Solution:            

Let the required distance be x km

Time taken to cover x km at 6 km/hr = x/6 hr

Time taken to cover x km at 4 km/hr = x/4 hr

According to the question, x/4 – x/6 = 10/60

⇒ x/4 – x/6 = 1/6

⇒ 3x – 2x /12 = 1/6

⇒ x/12 = 1/6     

⇒ x = 12/6          

Therefore, the required distance is 2 km.

Speed of Train

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction





8th Grade Math Practice

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