Question

The time taken by a person to travel an upward distance of 150 km was `2 1/2` hours more than the time taken in the downward return journey. If he returned at a speed of 10 km/h more than the speed while going up, find the speeds in each direction.

Answer 1

Given:

Distance (one way) = 150 km.

Time upward was `2 1/2` hours (i.e. 2.5 h) more than time downward.

Downward speed = (upward speed) + 10 km/h.

Step-wise calculation:

1. Let upward speed = x km/h.

Then downward speed = x + 10 km/h.

2. Time up = `150/x` hours. 

Time down = `150/(x + 10)` hours.

3. According to the problem:

`150/x = 150/(x + 10) + 2.5`

4. Rearrange the difference:

`150/x - 150/(x + 10) = 2.5`

`(150(x + 10) - x)/(x(x + 10)) = 2.5` 

`1500/[x(x + 10)] = 2.5`

5. So `x(x + 10) = 1500/2.5` 

= 600 

⇒ x² + 10x – 600 = 0

6. Solve the quadratic:

Discriminant = 10² – 4(1)(–600) 

= 100 + 2400 

= 2500

`x = (-10 ± 50)/2` 

Positive root: x = `(-10 + 50)/2` = 20 km/h (discard negative root)

Upward speed = 20 km/h.

Downward speed = 20 + 10 = 30 km/h.