Question

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 bus.

Answer 1

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.