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.

Answer 1

Let the speed of the rickshaw and the bus are x and y km/h, respectively.

Now, she has taken time to travel 2 km by rickshaw, t₁ = (2/x) hr

Speed = distance/ time

she has taken time to travel remaining distance i.e., (14 – 2) = 12km

By bus t₂ = (12/y) hr

By first condition,

t₁ + t₂ = ½ = (2/x) + (12/y) … (i)

Now, she has taken time to travel 4 km by rickshaw, t₃ = (4/x) hr

and she has taken time to travel remaining distance i.e., (14 – 4) = 10km, by bus = t₄ = (10/y) hr

By second condition,

t₃ + t₄ = ½ + 9/60 = ½ + 3/20

(4/x) + (10/y) = (13/20) …(ii)

Let (1/x) = u and (1/y) = v

Then Equations. (i) and (ii) becomes

2u + 12v = ½ …(iii)

4u + 10v = 13/20…(iv)

[First, multiply Eq. (iii) by 2 and then subtract]

(4u + 24v) – (4u + 10v) = 1–13/20

14v = 7/20

v = 1/40

Substituting the value of v in Eq. (iii),

2u + 12(1/40) = ½

2u = 2/10

u = 1/10

x = 1/u = 10km/hr

y = 1/v = 40km/hr

Hence, the speed of rickshaw = 10 km/h

And the speed of bus = 40 km/h.