Question

Ujjwal takes 3 hours more than Amit to walk 30 km but if ujwal Doubles his speed he is ahead of Amit by 3/2 hours. find the speed of walking

Answer 1

Answer:

Amit's speed is 5 km/h and Ujjwai's speed is 10/3 km/h

Step-by-step explanation:

Define x:

Let Amit takes x hours to walk 30 km

Ujjwai takes (x + 3) hours to walk 30 km

Find the speed of of Amit:

Speed = Distance ÷ Time

Speed = 30/x

Find the speed of Ujjwat:

Speed = Distance ÷ Time

Speed = 30/(x + 3)

If Ujjwai doubles his speed:

Speed = 30/(x + 3)  x 2

Speed = 60/(x + 3)

Find the time Ujjwai took

Time = Distance ÷ Speed

TIme = 30 ÷ 60/(x + 3) = (x + 3)/2

Solve x:

Ujjwai is 3/2 hour faster

x - (x + 3)/2 = 3/2

2x - (x + 3) = 3

2x - x - 3 = 3

x = 6 hours

Find the time each of them took:

Amit = x = 6 hours

Ujjwai = x + 3 = 6 + 3 = 9 hours

Find their speed:

Speed = Distance ÷ Time

Amit's  speed = 30 ÷ 6 = 5 km/h

Ujjwai's speed  = 30/9 = 10/3 km/h

Answer: Amit's speed is 5 km/h and Ujjwai's speed is 10/3 km/h

Answer 2

Answer:

Speed of Ujjwal  = 6.67 kph

Step-by-step explanation:

Let say

Hours taken by Amit  to walk 30 km = x

Hours taken by Ujjwal  to walk 30 km = x + 3

As we know

Distance covered by Ajjwal = Distance covered by Amit ...(1)

As

$Distance = speed*time$

So equation (1) would become

v₁ (x + 3) = v₂ (x) ....(2)

Now After Ujwal doubles his speed

Time taken by Ujwal = $x -\frac{3}{2}$

So, again as we know distance covered as same so our new equation is

2v₁ ($x-\frac{3}{2}$) = v₂ (x)

v₁ (2x - 3) = v₂ (x) .... (3)

Comparing equation 2 and 3

v₁ (2x - 3) = v₁ (x + 3)

cancelling same terms on both sides

2x - 3 = x + 3

2x - x = 3 + 3

x = 6 hours

So, it means initially

Time take by Amit to travell 30km = 6 hours

Speed of Amit = 30 ÷ 6 = 5 kph (Kilometer per hour)

Time take by Ujjwal to travell 30km = 6 + 3 = 9 hours

Speed of Ujjwl = 30 ÷ 9 = 3.34 kph (Kilometer per hour)

However, later on

Speed of Ujjwal = 2 x Initial Speed of Ujjwal

Speed of Ujjwal = 2 x 3.34 = 6.67 kph

Time take by Ujjwal to travell 30km = 6 - (3÷2) = 4.5 hours