Question

- A takes 3 h more than B in walking 30 km. If A doubles his speed, he will take 2 h less than B.
Assuming the speed of A to be x km/h, obtain an equation. Also, find the speeds of A and B.

Answer 1

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Step-by-step explanation:

Let the speed of A and B be x km/hr and y km/hr

Time taken by A to cover 30km

x

30

hrs

Time taken by B to cover 30km

y

30

hrs

According to the question

⇒

x

30

−

y

30

=3

⇒

x

10

−

y

10

=1...eq1

If A double his pace then the speed of A is 2x km/hr

therefore time taken by A to cover the 30 = 30/2xhrs And time taken by B to cover the 30KM = 30/yhrs

Now according to the question

⇒

y

30

−

2x

30

=

2

3

⇒

y

10

−

x

5

=

2

1

⇒−

x

10

+

y

20

=1...eq2

Now we assume

x

1

=u and

y

1

=v

Putting the u and v in eq1 and eq 2 we get

⇒10u−10v=1...eq3

⇒−10u+20v=1...eq4

Adding eq3 and eq4 we get

⇒10v=2

⇒v=

10

2

⇒v=

5

1

=

y

1

→y=5

Put v=

5

1

in eq3

⇒10u−3=0

⇒u=

10

3

=

x

1

⇒x=

3

10

Hence, the speed of A = 10\3 km/hr

The speed of B=5 km/hr respectively