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Q.19. Case study 3

Places A and B are 100 km apart on a highway. One car starts from A and another

from B at the same time. If the cars travel in the same direction at different speeds,

they meet in 5 hours. If they travel towards each other, they meet in 1 hour.

Let speed of the car- i is x km/hr and that of car- ii be y km/hr. then answer the

following

(i) What is the value of x

a) 60 km/hr

b) 65 km/hr

c) 70 km/hr

d) 75 km/hr

(ii) What is the value of y.

a) 50 km/hr

b) 20 km/hr

c) 40 km/hr

d) None of the above

(iii) What is x- y?

a) 30

b) 20

c) 10

d) 40

(IV) What is x + y?
a) 110

b) 85

c) 120

d) 100​​​​​

Answer 1

Let the speed of car at A be x kmph

and the speed of car at B be y kmph

when the car travel in same direction Relative Speed is x−y

Dist=100km

⟾ =5 hours

∴  Dist =S×T

⟾ 100=(x−y)5

⟾ x−y=20⟶(I)

when car travel in opp direction Relative Speed is x+y

⟾ Dist=100km

⟾ t=1 hours

⟾ Dist=ST

⟾ 100=(x+y)1

⟾ x+y=100⟶(II)

Solving (I) & (II)  ⟾ x−y=20

⟾ x+y=100

​⟾ 2x=120

⟾ x=60km/h

⟾ y=40km/h

Speed of the car at A =60 km/h

Speed of the car at B=40 km/h

The difference of speeds is 60−40=20