Calculating New Speed: Distance, Time, and Speed Problem

The problem asks for the required speed of a horse to cover a certain distance in a new timeframe, given its initial speed and time.

Step 1: Calculate the Total Distance

First, find the distance the horse covers using the initial speed and time. The formula for distance is:

$ \text{Distance} = \text{Speed} \times \text{Time} $

Given:

• Initial Speed = 40 km/h
• Initial Time = 3 h

Calculation:

$ \text{Distance} = 40 \, \text{km/h} \times 3 \, \text{h} = 120 \, \text{km} $

Step 2: Calculate the New Required Speed

Next, calculate the speed needed to cover the same distance (120 km) in the new time ($2\frac{1}{2}$ hours).

The formula for speed is:

$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $

Given:

• Distance = 120 km
• New Time = $2\frac{1}{2}$ h = 2.5 h

Calculation:

$ \text{New Speed} = \frac{120 \, \text{km}}{2.5 \, \text{h}} $

To simplify the division:

$ \text{New Speed} = \frac{120}{5/2} \, \text{km/h} = 120 \times \frac{2}{5} \, \text{km/h} = \frac{240}{5} \, \text{km/h} = 48 \, \text{km/h} $

Therefore, the horse should run at a speed of 48 km/h.