Question

2. In travelling from home to school, Natalie took a bus for two fifths of the journey, a taxi for one third of the journey and walked for the rest of the journey.

(i) What fraction of the journey was spent in travelling by bus and by taxi?
(ii) What fraction of the journey was spent walking?
(iii) Natalie travelled for 5 km in the taxi, what is the total distance from home to school?

Answer 1

Given :

In travelling from home to school, Natalie took a bus for two fifths of the journey, a taxi for one third of the journey and walked for the rest of the journey.

To Find :

1. What fraction of the journey was spent in travelling by bus and by taxi?
2. What fraction of the journey was spent walking?
3. Natalie travelled for 5 km in the taxi, what is the total distance from home to school?

Solution :

Let the total journey be “x” km.

So,

• Fraction of journey spent on bus = 2/5 of x = 2/5 × x = 2x/5 km
• Fraction of journey spent on taxi = 1/3 of x = 1/3 × x = x/3 km

(i)

Fraction of journey spent by travelling in bus and taxi,

= 2x/5 + x/3

= (6x + 5x)/15

= 11x/15

Fraction of journey spent by travelling in bus and taxi is 11x/15 km.

(ii)

It is said that in travelling from home to school, Natalie took a bus for two fifths of the journey, a taxi for one third of the journey and walked for the rest of the journey.

So,

Fraction of journey spent walking,

= x - 11x/15

= (15x - 11x)/15

= 4x/15

Fraction of journey spent walking is 4x/15 km.

(iii)

Natalie travelled for 5 km in taxi.

Fraction of journey travelled by taxi is 1/3 of x.

ATQ,

⇒ 1/3 of x = 5

⇒ 1/3 × x = 5

⇒ x/3 = 5

⇒ x = 5 × 3

⇒ x = 15

∴ x = 15 km.

Total distance from home to school is 15 km.