- Preeti travels 500 km to his home partly by car and partly by bus. She takes 11 hrs if she travels 300 km by car and the rest by bus. She takes 12 hrs if she travels 100 km by car and the rest by bus. Find the speed of the car and the bus.
Answers
Answer:
120 km speed second hours
Answer:
Speed of Car
Step-by-step explanation:
Let the speed of car be x. And the speed of bus be y.
A.T.Q.
Case-1
11 = 300/x + 200/y
11 = 300y + 200x / xy
11xy = 300y + 200x
xy = 300y + 200x / 11. --------------(1)
Case-2
12 = 100/x + 400/y
12 = 100y + 400x / xy
xy = 100y + 400x / 12. -----------------(2)
Equating equ.1 & 2
300y + 200x / 11 = 100y + 400x / 12
12(300y + 200x) = 11(100y + 400x)
3600y + 2400x = 1100y + 4400x
3600y - 1100y = 4400x - 2400x
2500y = 2000x
5y = 4x
x = 5y/4. ------(3)
Putting the value of y in equ.2
xy= 100y + 400x / 12
(5y/4)y = 100y + 400(5y/4) / 12
5y^2 / 4 = 100y + 500y / 12
5y^2 / 4 = 600y / 12
5y^2 = 600y / 3
5y^2 = 200y
5y = 200
y = 40
Putting y = 40 in equ.3
x = 5y/4
x = 5 × 40 / 4
x = 5 × 10
x = 50
Therefore, the speed of car is 50 km/hr. & the of bus is 40 km/hr.
Answer:
Speed of Car = 50 km/hr.
Speed of Bus = 40 km/hr.
Step-by-step explanation:
Let the speed of car be x. And the speed of bus be y.
A.T.Q.
Case-1
11 = 300/x + 200/y
11 = 300y + 200x / xy
11xy = 300y + 200x
xy = 300y + 200x / 11. --------------(1)
Case-2
12 = 100/x + 400/y
12 = 100y + 400x / xy
xy = 100y + 400x / 12. -----------------(2)
Equating equ.1 & 2
300y + 200x / 11 = 100y + 400x / 12
12(300y + 200x) = 11(100y + 400x)
3600y + 2400x = 1100y + 4400x
3600y - 1100y = 4400x - 2400x
2500y = 2000x
5y = 4x
x = 5y/4. ------(3)
Putting the value of y in equ.2
xy= 100y + 400x / 12
(5y/4)y = 100y + 400(5y/4) / 12
5y^2 / 4 = 100y + 500y / 12
5y^2 / 4 = 600y / 12
5y^2 = 600y / 3
5y^2 = 200y
5y = 200
y = 40
Putting y = 40 in equ.3
x = 5y/4
x = 5 × 40 / 4
x = 5 × 10
x = 50
Therefore, the speed of car is 50 km/hr. & the of bus is 40 km/hr.
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