# 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 the bus in km/hr respectively.

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Updated on: September 25th, 2023

(a) 10 km/hr, 30 km/hr

(b) 10 km/hr, 40 km/hr

(c) 30 km/hr, 10 km/hr

(d) 40 km/hr, 10 km/hr

The speed of the rickshaw and the bus in km/hr respectively is 10 and 40. Let the bus’s speed be y km/min and the rickshaw’s speed be x km/min:

As time = distance/speed,

2/x + 12/y = 30

4/x + 10/y = 39

Substitute 1/x as u and 1/y as v, we get (where x ≠ 0, y ≠ 0)

2u + 12v = 30 …. (1)

4u + 10v = 39 ….. (2)

Multiply (1) by 2, and we get

4u + 24v = 60 …. (3)

Subtract (2) from (3), we get 14v = 21

v = 3/2

Substitute v = 3/2 in (1) we get

2u + 12 x 3/2 = 30

2u = 30 – 18

u = 12/2 = 6

x = ⅙ km/min and y = ⅔ km/min

To find the speed in km/hr, we should multiply the speed by 60, as 1 hr = 60 min.

Hence,

x = ⅙ x 60 = 10 km/hr

y = ⅔ x 60 = 40 km/hr

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. Find the speed of the rickshaw and the bus in km/hr respectively.

Ankita goes 14 miles to get home, taking the bus and rickshaw in turns. If she travels 2 km by rickshaw and the final 3 km by bus, it will take her 30 minutes. On the other hand, it takes her 9 minutes longer if she goes 4 km by rickshaw and the remaining distance by bus. The bus travels at a speed of 40 km/h and the rickshaw at 10 km/h, respectively.

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