The distance that an object travels is equal to the product of the average speed at which it travels and the time it takes to travel that distance. Rate is another word used in place of speed. Mathematically,
Speed × Time = Distance
ST = D
Any problem involving distance, speed, or time spent travelling can be boiled down to this equation. The important thing is that you have your variables and numbers plugged in properly.
For a single trip at one speed, the question is very simple. This concept becomes much more complex when the question involves two trips, in which the car travels at one speed in one trip, and at another speed in another trip. Simply averaging the two velocities will give wrong answer.
You always need to apply ST = D separately in each part of the trip, and then you need to add results from the individual legs to find the total distance and the total time. And then apply the formula for average speed.
Example 1: If a car travels at an average speed of 70 kilometers per hour for 4 hours, how many kilometers does it travel?
Since rate x time = distance, multiply 70 km/hr x 4 hr. Thus, the car travels 280 kilometers in 4 hours.
Example 2: On a 400-mile trip, Car X traveled half the distance at 40 miles per hour (mph) and the other half at 50 mph. What was the average speed of Car X?
First, determine the amount of travelling time. During the first 200 miles, the car travelled at 40 mph; therefore, it took 5 hours to travel the first 200 miles.
During the second 200 miles, the car travelled at 50 mph; therefore, it took 4 hours to travel the second 200 miles. Thus, the average speed of Car X was 400/9 mph.
Example 3: If 5 shirts cost $44, then, at this rate, what is the cost of 8 shirts?
If c is the cost of the 8 shirts, then 5/44 = 8/c. Cross multiplication gives 5c = 352. The 8 shirts cost $70.40.