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A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
- a)100 Km
- b)110 Km
- c)120 Km
- d)140 Km
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A walks with a speed of 6 km/hr and after 5 hr of his start, B starts ...
In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.
x/6 = (30+x)/8
x = 90. So distance from start after which B will catch A = 90+30 =120km
x/6 = (30+x)/8
x = 90. So distance from start after which B will catch A = 90+30 =120km
Most Upvoted Answer
A walks with a speed of 6 km/hr and after 5 hr of his start, B starts ...
Problem: A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
Solution:
Let the distance traveled by A be x km.
Time taken by A to travel x km = x/6 hours
As B starts after 5 hours of A's start, time taken by B to catch A = (x/6) - 5 hours
Speed of B = 8 km/hr
Distance traveled by B in (x/6) - 5 hours = 8 [(x/6) - 5] km
Distance traveled by A in (x/6) - 5 hours = (x/6) [(x/6) - 5] km
As B catches A, distance traveled by B = distance traveled by A
So, 8 [(x/6) - 5] = (x/6) [(x/6) - 5]
8x/6 - 40 = x^2/36 - 5x/6
Multiplying by 36 on both sides,
12x - 720 = x^2 - 30x
x^2 - 42x + 720 = 0
(x - 12) (x - 60) = 0
As distance can't be negative, x = 60 km
Therefore, B catches A at a distance of 60 km from the start.
Hence, the correct answer is option (c) 120 km.
Solution:
Let the distance traveled by A be x km.
Time taken by A to travel x km = x/6 hours
As B starts after 5 hours of A's start, time taken by B to catch A = (x/6) - 5 hours
Speed of B = 8 km/hr
Distance traveled by B in (x/6) - 5 hours = 8 [(x/6) - 5] km
Distance traveled by A in (x/6) - 5 hours = (x/6) [(x/6) - 5] km
As B catches A, distance traveled by B = distance traveled by A
So, 8 [(x/6) - 5] = (x/6) [(x/6) - 5]
8x/6 - 40 = x^2/36 - 5x/6
Multiplying by 36 on both sides,
12x - 720 = x^2 - 30x
x^2 - 42x + 720 = 0
(x - 12) (x - 60) = 0
As distance can't be negative, x = 60 km
Therefore, B catches A at a distance of 60 km from the start.
Hence, the correct answer is option (c) 120 km.
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