26.
To save fuel, to avoid air pollution and for good health two persons A and B
ride bicycle for a distance of 12 km to reach their office. As the cycling
speed of B is 2 km/h more than that of A, B takes 30 minutes less than
that of A to reach the office. Find the time taken by A and B to reach the
office.
Answers
Answer:
Time taken by A to reach office = 2 hrs.
Time taken by B to reach office = 1 hr 30 mins.
Step-by-step explanation:
Let the speed of A be 'x' km/h.
So, speed of B = (x + 2) km/h
Now,
Distance = 12 km
We know that,
Speed = Distance/Time
So,
Time = Distance/Speed
Time taken by A = 12/x
Time taken by B = 12/(x + 2)
Now, according to the Question,
Time taken by A - Time taken by B = 30 mins.
Now, we have consider everything in hours, so we must changes mins. to hrs.
60 mins = 1 hr.
1 min. = (1/60) hr.
Then,
30 mins. = 30 × (1/60)
30 mins. = 30/60
30 mins. = (1/2) hr.
So, according to the Question,
(12/x) - (12/(x + 2)) = (1/2)
Taking 12 common,
12 [(1/x) - (1/(x + 2))] = (1/2)
12 [((x + 2) - x)/(x(x + 2))] = (1/2)
12 [(x + 2 - x)/(x² + 2x)] = (1/2)
12 [2/(x² + 2x)] = (1/2)
24/x² + 2x = (1/2)
Cross multiplying we get,
2 × 24 = 1 × (x² + 2x)
48 = x² + 2x
x² + 2x - 48 = 0
ax² + bx + c = 0
where a = 1, b = 2, c = -48
Using the Quadratic formula,
x = ((-b) ± √(b² - 4ac))/2a
x = ((-2) ± √(2² - 4(1)(-48)))/2(1)
x = ((-2) ± √(4 + 192))/2
x = ((-2) ± √(196))/2
x = ((-2) ± 14)/2
x = ((-2) + 14)/2 or x = ((-2) - (14))/2
x = 12/2 or x = (-16)/2
x = 6 or x = (-8)
We know that speed can't be negative so,
x = 6 km/h
So,
Speed of A = 6 km/h
Speed of B = (6 + 2) = 8 km/h
Therefore,
Time taken by A = 12/6 = 2 hrs.
Time taken by B = 12/8 = 1.5 hrs.
Hence,
Time taken by A to reach office = 2 hrs.
Time taken by B to reach office = 1 hr 30 mins.
Hope it helped and believing you understood it........All the best
Answer:
Given : A and B ride bicycle for a distance of 12km to reach their office. As cycling speed of B is 2 km/h more than that of A, B takes 30 minutes less than that of A to reach the office.
To find : the time taken by A and B to reach the office
Proof :
Distance of Office =12 km
Speed of A = S km/hr
Speed of B = S + 2 km/hr
Time taken by A = 12/S hr
Time Taken by B = 12/(S + 2) hr
B takes 30 minutes less than that of A to reach the office.
30 minutes = 1/2 hr
=>12/(S + 2) = 12/S - 1/2
=> 12*2S = 12*2(S + 2) - S(S + 2)
=> 24S = 24S + 48 - S² - 2S
=> S² + 2S - 48 = 0
=> S² + 8S - 6S - 48 = 0
=> S(S + 8) - 6(S + 8) = 0
=> (S - 6) (S + 8) = 0
=> S = 6 , S = - 6
Speed of A = 6 km/hr
Speed of B = 8 km/hr
Time taken by A = 12/6 = 2 hr
Time taken by B = 12/8 = 1.5 hr
Time taken by A and B to reach the office are 2 hr & 1.5 hr respectively