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28 Dec 2021, 09:45
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Difficulty:
95%
(hard)
Question Stats:
31% (01:34) correct
69%
(03:19)
wrong
based on 68
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Three cars travel from destination A to destination B in equal time intervals. They reach B simultaneously and then leave for destination C which is 240 miles away from destination B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 miles away from C. What is the difference between the speed (in miles per hour) of the first and the third car?
A. 20
B. 35
C. 40
D. 60
E. 80
Are You Up For the Challenge: 700 Level Questions
A. 20
B. 35
C. 40
D. 60
E. 80
Are You Up For the Challenge: 700 Level Questions
03 Feb 2022, 09:52
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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
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
24 Jun 2024, 02:16
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Quote:
how did you arrive at this equation ?
