Question

Q) 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. What are the speeds of the two cars?

Answer 1

Answer:

let the speed of first car=x km/h

let the speed of second car=y km/h

total distance = 100 km

(both travels in same direction)

speed of cars = (x-y) km/h

distance = 100km

time taken = 5hr

speed= distance/ time

x-y=100/5

x-y=20------1

(both travels in opposite directions)

speed of cars = (x+y) km/h

distance = 100 km

time taken = 1hr

speed= distance/time

x+y= 100/1

x+y=100--------2

taking eq 2 & 1

x+y=100

x-y=20

2x= 120

x=60

substitute x=60 in eq 2

x+y= 100

60+y= 100

y= 100-60

y=40

the speed of first car is 60km/hr

the speed of second car is 40 km/hr

Answer 2

Answer:

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Let the speed of car at A be x km/h

and the speed of car at B be y km/h

As per the question,

5x - 5y = 100

x - y = 20 ... (1)

and x + y = 100 ... (2)

Solving (1) and (2), we get,

x = 60 and y = 40

Speed of the car at A = 60 km/h

Speed of the car at B = 40 km/h