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.
Similar Questions
- A man driving a car at a speed of 79 km/hr crosses a bridge in 3.6 minutes. Find the length of the bridge.
- Rohan can travel from Delhi to Kanyakumari in 30 h. If he reduces his speed by $\frac{1}{15}$th, he goes 10 km less in the same time. Find the speed.
- How many poles will be covered by a train in 4 hours if the train is running at a speed of 45 km/hr, given that the poles on the railway track are 50 m apart and the train crosses a pole at the beginning of its journey.
- The speeds of three trains are in the ratio of 2 : 3 : 5. The amount of time taken by these trains to travel the same distance is in the ratio of:
- Two persons A and B start a journey from the same point at the speeds of 3 km/h and 4 km/h respectively. If they move in the same direction, then what will be the distance between them after 6 h?
- Train A leaves station M at 6:25 AM and reaches station N at 3:25 PM on the same day. Train B leaves station N at 8:25 AM and reaches station M at 2:25 PM on the same day. Find the time when trains A and B meet.
- If a train runs at an average speed of 42 km/h, then it covers a certain distance in 45 min. What is the speed at which the train must run to reduce the time of the same journey to 35 min?
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Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
