Question

Travelling at 80 kmph a person can reach his destination in a certain time. He covers 3 /4 of the journey in 4/ 5 of the total time. At what speed should he travel the remaining distance to reach his destination on time?

Answer 1

Answer:

100 km/h

Step-by-step explanation:

We can solve this in two ways, I will show you both ways, so here we go.........

Method 1

Let the Total Distance for the Journey be 'D' km and Total Time be 'T' hrs

Thus,

D/T = 80 km/h ---- 1

Now,

According to the Question,

He travelled 3/4 of the distance in 4/5 of time

That is, (3/4)D in (4/5)T

Now, distance left = D - (3/4)D

= (4/4)D - (3/4)D = (1/4)D

and time left = T - (4/5)T

= (5/5)T - (4/5)T = (1/5)T

Thus, we need to find the speed required to travel (1/4)D in (1/5)T

Speed = Distance/Time

= (1/4)D ÷ (1/5)T

= D/4 × 5/T

= 5/4(D/T)

From eq.1 we get D/T = 80 km/h

Speed = (5/4) × (80)

Speed = 100 km/h

Thus, he must travel with a speed of 100 km/h to reach his destination on time.

Method 2

We know that,

Total Distance covered ÷ Total time taken = 80km/h

Let the certain time mentioned here be 'x' hrs

Speed = Distance/Time

then,

Distance = Speed × Time

Distance = 80 × x = 80x km

Now,

He covers 3/4 of the distance in 4/5 of the time

so, Distance covered = 80x × (3/4) = 60x km

and the time taken = x × (4/5) = (4/5)x

Now the distance left = 80x - 60x = 20x km

So, he has 20x km more to finish his journey

Time left = x - (4/5)x = (5/5)x - (4/5)x = (1/5)x

So, he has (1/5)x more to finish his journey

Now,

He has to complete 20x km in (1/5)x hrs

then,

Speed = 20x/(1/5)x = 20x ÷ (1/5)x

= 20x × (5/x) = 20 × 5 = 100 km/h

Thus, he must move with a speed of 100 km/h to reach the destination on time.

Hope it helped and you understood it........All the best