Calculating Travel Time for Cars at Different Speeds

Understanding how to calculate travel time based on speed and distance is essential for efficient road travel. Whether you are commuting or planning a journey, knowing the relationship between speed, distance, and time is crucial. This article will guide you through the calculations step by step using various examples.

Example 1: Traveling 30 km at 90 km/h

Let's consider a car traveling at 90 km/h. We need to find out how much time it will take to cover a distance of 30 km.

Using the basic formula of distance speed × time, we can rearrange it to calculate time.

First, convert the distance to a fraction of the total speed:

90.3 27

So, 30 km is a fraction of 90 km/h. Specifically, it is frac{1}{3} of the speed.

The time taken is given by t frac{d}{s}, where d30d 30, s90s 90, so t frac{30}{90} frac{1}{3}

This fraction of time translates to 0.3 hours. To find minutes, multiply by 60:

13frac{1}{3} frac{30}{60} u2192 18 minutes

Thus, it will take 18 minutes to travel 30 km at 90 km/h.

Example 2: A 30-minute Journey at 100 km/h

Another example is a car traveling at 100 km/h for 30 minutes. We need to find the distance covered.

First, convert the time from minutes to hours:

30 minutes 30 / 60 0.5 hours

Now, use the formula for distance:

Distance Speed × Time 100 km/h × 0.5 h 50 kmtext{Distance Speed }times text{Time} 100 text{ km/h } times 0.5 text{ h} 50 text{ km}

Hence, the car will cover 50 km in 30 minutes at 100 km/h.

Example 3: Distance Covered in 30 Minutes at 90 km/h

Let's find the distance covered by a car traveling at 90 km/h in 30 minutes.

Using the formula from Example 1, we know 30 minutes is 0.5 hours.

Distance Speed math>times Time 90 km/h × 0.5 h 45 kmtext{Distance Speed }times text{Time} 90 text{ km/h } times 0.5 text{ h} 45 text{ km}

However, the numerator (distance) should be 27 km, which implies the speed is adjusted to 54 km/h for 27 km. But for the original 90 km/h, the distance is 45 km.

Therefore, the car will cover 45 km in 30 minutes at 90 km/h.

Example 4: 30 Minutes at 100 km/h Revisited

We can also use a different approach to find the distance covered in 30 minutes at 100 km/h:

Rate 100 km/hr, Time 30 min (0.5 hr, as calculated earlier), Distance Rate × Time:

Distance Speed × Time 100 km/h × 0.5 h 50 kmtext{Distance Speed }times text{Time} 100 text{ km/h } times 0.5 text{ h} 50 text{ km}

This confirms that the car will cover 50 km in 30 minutes at 100 km/h.

Summary

In conclusion, by using the formula Distance Speed × Timetext{Distance Speed }times text{Time}, we can accurately determine the distance covered in a given time, or the time taken to cover a certain distance, given the speed. These calculations are applicable to various scenarios, be it personal travel, road planning, or even professional logistics.

Understanding these fundamental concepts will help in better road management and efficient travel.