Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus
Solution:
Let the speed of the rickshaw be x km/h
Let the speed of the bus be y km/h.
Time taken to travel 2 km by rickshaw,
t₁ = 2/x hours.
Time taken to travel the remaining distance
(14 - 2) = 12 km by bus,
t₂ = 12/y hours.
According to first condition,
t₁ + t₂ = 1/2.
2/x + 12/y = 1/2-------------------------------(1)
Time taken to travel 4 km by rickshaw,
t₃ = 4/x hours.
Time taken to travel remaining distance (14 - 4) = 10 km by bus,
t₄ = 10/y hours.
According to the second condition,
t₃ + t₄ = 1/2 + 9/60 = 1/2 + 3/20.
4/x + 10/y = 13/20-----------------------------(2)
Consider
1/x = u,
1/y = v.
Rearranging the equation, we get,
2u + 12ν = 1/2 ------------------------(3)
4u + 10ν = 13/20----------------------(4)
Solve the linear equations (3) and (4)
Multiplying (3) by 2 and then subtracting (4), we get,
(4u + 24v) - (4u + 10v) = 1-13/20
14v = 7/20
2v = 1/20
v = 1/20.
Substituting the value of v in (3),we get,
2u + 12(1/40) = 1/2.
2u = 1/2 - 3/10
2u = 5-3/10
2u = 2/10
u = 1/10.
1/x = = 1/10
x = 10.
1/y = 1/40
y = 40.
x = 10.
y = 40.
Therefore, the speed of the rickshaw and the bus are 10 km/h and 40 km/h, respectively.
✦ Try This: Ankita travels 15 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 3 km by rickshaw, and the remaining distance by bus.On the other hand, if she travels 2 km by rickshaw and the remaining distance by bus, she takes 10 minutes longer. Find the speed of the rickshaw and of the bus
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 6
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus
Summary:
Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. The speed of the rickshaw and the bus are 10 km/h and 40 km/h, respectively
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