Question

A car travel P to Q at a constant speed.if its speed increase by 10km/h,it would have been taken 1 hr lesser to cover everything distance. it would have been taken 45 min.lesser by further increase the speed by 10 km/hr .find the distance between two cities.

Answer 1

Answer:

420 km

Step-by-step explanation:

Let distance = x km and usual rate = y km/hr. Then

y

x

−

y+10

x

=1

⇒

y(y+10)

xy+10x−x

=1

⇒10x−y

2

−10y=0

⇒y

2

+10y−10x=0⟶(1)

and

y

x

−

y+20

x

=

4

7

y(y+20)

xy+20x−xy

=

4

7

80x=7y

2

+140y

7y

2

+140y−80x=0⟶(2)

On dividing (1) by (2) we get y=60

Substituting y=60 in (1) we get

60

2

+10(60)−10x=0

3600+600−10x=0

x=420 km.

So required distance is 420 km.