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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