3 cars leave Begusarai for Patna after equal interval of time.They reach Patna simultaneously and then leave for Ara , which is 126 km from Patna.The first car arrives there1/4 hour after second car and third car having reached Ara, immediately reverse the direction and 18 km from Ara meets the first car.Find the speeds of all the cars.
Answers
Answer:
60 km/Hr
Step-by-step explanation:
Let say Speed of Car1 = X km/Hr
Let say Speed of Car2 = Y km/Hr
Let say speed of car3 = Z km/Hr
Let say distance between AB = D km/Hr
Time taken by Car 1 = D/X
Time taken by Car 2 = D/Y
Time taken by Car 3 = D/Z
D/Z - D/Y = D/Y - D/X
=> 2/Y = 1/X + 1/Z - eq 1
Time taken by car 2 for 240 km = 240/Y
Time taken by Car 1 for 240 km = 240/X
240/X = 240/Y + 1
=> 1/X - 1/240= 1/Y - eq 2
Putting 1/Y in eq 1
2/X - 1/120 = 1/X + 1/Z
=> 1/X = 1/Z + 1/120 - eq 3
When 1st & Third car meet
Distance traveled by third car = 240 + 80 = 320 km
Distance traveled by First Car = 240 - 80 = 160 km
Time taken by both car is equal
320/Z = 160/X
=> Z = 2X
putting in eq 3
=> 1/X = 1/2X + 1/120
multiplying by 120X
=> 120 = 60 + X
=> X = 60
Z = 2X = 120
Z - X = 120 - 60 = 60 km/Hr
difference between the speed of the first and the third car = 60 km/Hr