Two cars A and B start from P with uniform speed and reach Q. The total time taken by both the cars is 10 hour. If A starts from P and B starts from Q, then they meet at a point in between P and Q in 2h 24min . If the distance between P and Q is 360 km., then find the difference in speed of cars (in KMPH);
(1) 10
(2) 15
(3) 30
(4) 20
Pls answer with complete explanation.
Answers
speed of car B = y kmph
Distance between P and Q = 360 km
Time taken to reach A to Q :
by car A ( t1) = 360/x hr
car B ( t2 ) = 360/y he
Total time taken by two cars = 10 hr
360/x + 360/y = 10
=> 360( 1/x + 1/y ) = 10
=> 1/x + 1/y = 1/36
=> ( x + y )/xy= 1/36 ---( 1 )
ii ) If cars travel in opposite directions,
time taken to meet ( t ) = 2 hr 24 mi
= 2 + 24/60
= 2 + 2/5
= 12/5 hr
Distance covered in 12/5 hrs by
car A ( d1 ) = speed × time
= 12x/5
Distance covered by car B(d2) = 12y/5
d1 + d2 = 360
=> 12x/5 + 12y/5 = 360
=> 12/5( x + y ) = 360
=> x + y = ( 360 × 5 )/12
=> x + y = 150 ------( 2 )
Put x + y = 150 in equation ( 1 ), we get
150/xy = 1/36
=> xy = 36 × 150 ----( 3 )
Now ,
( x - y )² = ( x + y )² - 4xy
= ( 150 )² - 4 × 36 × 150
= 22500 - 21600
= 900
x - y = √900
=> x - y = 30
Therefore ,
Difference of Two cars speeds = 30 kmph
Option ( 3) is correct.
•••••
Answer:
30 km/h
Step-by-step explanation:
Define x:
Let the time taken for car A be x
The time taken for car B is (10 - x)
Find the speed of Car A and Car B:
Speed = Distance ÷ Time
Speed of Car A = 360/x
Speed of Car B = 360/(10 - x)
Find their total speed when they travel in opposite direction:
Time = 2h 24 mins = (2 + 24/60)h = 2.4 hours
Speed = Distance ÷ Time
Speed = 360 ÷ 2.4 = 150 km/h
Solve x:
360/x + 360/(10 - x) = 150
360(10 - x) + 360x = 150x(10 - x)
3600 - 360x + 360x = 1500x - 150x²
150x² - 1500x + 3600 = 0
x² - 10x + 24 = 0
(x - 4)(x - 6) = 0
x = 4 or x = 6
If x = 4,
Speed of Car A = 360/4 = 90 km/h
Speed of car B = 360/6 = 60 km/h
Difference = 30 km/h
If x = 6,
Speed of Car A = 360/6 = 60 km/h
Speed of Car B = 360/4 = 90 km/h
Difference = 30 km/h
Answer: (3) 30 km/h