Time and Distance

Math-home

Question (3) A cyclist covers 2/3 of a journey at a speed of 4 km/h and rest at a speed of 5 km/h. It he takes 7 hour in total journey, then find the distance of the journey.

Solution

Given, total time in the journey (t) = 7 hour

Speed of while travelling 2/3 of the journey = 4 km/h

And, speed in rest of the journey, i.e. 1/3 of the journey = 5 km/h

Thus, total distance covered = ?

Let the total distance of the journey = p km

Thus, distance of 2/3 of the journey `=2/3xxp\ km`

Rest of the journey

Now, we know that, time (t) = Distance / Speed

Thus, time taken in 2/3 of the journey

And time taken in 1/3 of the journey

As given, total time = 7 hour

Thus, time taken to cover total distance = time taken to cover 2/3 of the journey + time taken to cover 1/3 of the journey

⇒ p = 30 km

Thus, total distance = 30 km Answer

Question (4) A cyclist covers 4/5 of a journey at a speed of 8 km/h and rest at a speed of 2 km/h. It he takes 10 hour in total journey, then find the distance of the journey.

Solution

Given, total time in the journey (t) = 10 hour

Speed of while travelling 4/5 of the journey = 8 km/h

And, speed in rest of the journey, i.e. 1/5 of the journey = 2 km/h

Thus, total distance covered = ?

Let the total distance of the journey = p km

Thus, distance of 4/5 of the journey `=4/5xxp\ km`

And, rest of the journey, i.e. 1/5 of the journey `=p/5`

Now, we know that, time (t) = Distance / Speed

Thus, time taken in 4/5 of the journey

And time taken in 1/5 of the journey

As given, total time = 10 hour

Thus, time taken to cover total distance = time taken to cover 4/5 of the journey + time taken to cover 1/5 of the journey

⇒ p = 50 km

Thus, total distance = 50 km Answer

Alternate Method

As calculated above, equal time is taken in both of the journey.

This means half time has been taken to cover 4/5 part of the journey in which speed was 8 km/h and half time has been taken to cover 1/5 of the journey at a speed of 2 km/h.

Here half time means total time divided by 2.

= 10/2 = 5 hour

Thus, 5 hour is taken at a speed of 8 km/h, i.e. to cover the 4/5 of the distance.

Now, we know that,

Distance = Speed × Time

Thus, distance covered in first part of journey = 8 km/h × 5 h

= 40 km

And, 5 hour is taken at a speed of 2 km/h, i.e. to cover the 1/5 of the distance

Thus, distance covered in second part of journey

= speed × time

= 2 km/h × 5 h

= 10 km

Thus, total distance = 40 km + 10 km

= 50 km

Thus, total distance = 50 km Answer

Question (5) A cyclist covers 3/5 of a journey at a speed of 6 km/h and rest at a speed of 8 km/h. It he takes 9 hour in total journey, then find the distance of the journey.

Solution

Given, total time in the journey (t) = 9 hour

Speed of while travelling 3/5 of the journey = 6 km/h

And, speed in rest of the journey, i.e. 2/5 of the journey = 8 km/h

Thus, total distance covered = ?

Let the total distance of the journey = p km

Thus, distance of 3/5 of the journey `=3/5xxp\ km`

And, rest of the journey, i.e. 2/5 of the journey `=(2p)/5\ km`

Now, we know that, time (t) = Distance / Speed

Thus, time taken in 3/5 of the journey

And time taken in 2/5 of the journey

As given, total time = 9 hour

Thus, time taken to cover total distance = time taken to cover 3/5 of the journey + time taken to cover 2/5 of the journey

⇒ p = 60 km

Thus, total distance = 50 km Answer

Question (6) A cyclist covers 2/7 of a journey at a speed of 6 km/h and rest at a speed of 9 km/h. It he takes 8 hour in total journey, then find the distance of the journey.

Solution

Given, total time in the journey (t) = 8 hour

Speed of while travelling 2/7 of the journey = 6 km/h

And, speed in rest of the journey, i.e. 5/7 of the journey = 9 km/h

Thus, total distance covered = ?

Let the total distance of the journey = p km

Thus, distance of 2/7 of the journey `=2/7xxp\ km`

And, rest of the journey, i.e. 5/7 of the journey `=(5p)/7\ km`

Now, we know that, time (t) = Distance / Speed

Thus, time taken in 2/7 of the journey

And time taken in 5/7 of the journey

As given, total time = 8 hour

Thus, time taken to cover total distance = time taken to cover 2/7 of the journey + time taken to cover 5/7 of the journey

⇒ p = 63 km

Thus, total distance = 63 km Answer

Question (7) A cyclist covers 5/6 of a journey at a speed of 6 km/h and rest at a speed of 3 km/h. It he takes 9 hour in total journey, then find the distance of the journey.

Solution

Given, total time in the journey (t) = 9 hour

Speed of while travelling 5/6 of the journey = 5 km/h

And, speed in rest of the journey, i.e. 1/6 of the journey = 2 km/h

Thus, total distance covered = ?

Let the total distance of the journey = p km

Thus, distance of 5/6 of the journey `=5/6xxp\ km`

And, rest of the journey, i.e. 1/6 of the journey `=(p)/6\ km`

Now, we know that, time (t) = Distance / Speed

Thus, time taken in 5/6 of the journey

And time taken in 1/6 of the journey

As given, total time = 9 hour

Thus, time taken to cover total distance = time taken to cover 5/6 of the journey + time taken to cover 1/6 of the journey

⇒ p = 36 km

Thus, total distance = 36 km Answer

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Math-home

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