# 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.

Given

Distance travelled by Ankita to her home partly by rickshaw and partly by bus= 14km

She takes half an hour if she travels 2 km by rickshaw and the remaining distance by bus

Find out

We have to determine the speed of the bus and rickshaw

Solution

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

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

We know that

Speed = distance/ time

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

By bus t2 = (12/y) hr

By first given condition,

t+ t2 = ½ = (2/x) + (12/y) … (i)

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

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

By second given 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)

Let us first, multiply Eq. (iii) by 2 and then subtract

(4u + 24v) – (4u + 10v) = 1–13/20

14v = 7/20

v = 1/40

On 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.