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.

Relationship between Speed, Distance and Time

Problems on Calculating Distance

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

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

**8th Grade Math Practice**

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