Question

Kavita travels 28 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 4 km by rickshaw and the remaining distance by bus. If she travels 8 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed to rickshaw and the speed of the bus.

Answer 1

Given:

• Total distance Kavita travels = 28 km.
• First case: 4 km by rickshaw and remaining by bus with total time = 30 minutes.
• Second case: 8 km by rickshaw and remaining by bus with time 9 minutes longer than first case so 39 minutes.
• We want to find the speed of the rickshaw and the speed of the bus.

Step-wise calculation:

Let:

Speed of rickshaw = x km/h.

Speed of bus = y km/h.

First case:

Distance by rickshaw = 4 km.

Distance by bus = 28 – 4 = 24 km.

Time taken = 30 minutes = 0.5 hours.

So, `4/x + 24/y = 0.5`   ...(1)

Second case:

Distance by rickshaw = 8 km.

Distance by bus = 28 – 8 = 20 km.

Time taken = 30 + 9 = 39 minutes = `39/60` = 0.65 hours.

So, `8/x + 20/y = 0.65`   ...(2)

Multiply (1) by 2 to make elimination easier:

`8/x + 48/y = 1`   ...(3)

Subtract (2) from (3):

`(8/x + 48/y) - (8/x + 20/y) = 1 - 0.65`

`48/y - 20/y = 0.35`

`28/y = 0.35`

⇒ `y = 28/0.35`

⇒ y = 80 km/h

Now substitute (y = 80) in (1):

`4/x + 24/80 = 0.5`

`4/x + 0.3 = 0.5`

`4/x = 0.2`

⇒ `x = 4/0.2`

⇒ x = 20 km/h

Speed of the rickshaw = 20 km/h.

Speed of the bus = 80 km/h.