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.
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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.
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