Question

Identify the type of proportion that the following problems illustrate. Then solve theproblems in a piece of paper,

1.) A car is able to travel 210 km in 3 hours. How far can it travel in 5 hours?
2.) Five people can finish painting a wall in 5 hours. I only 2 people are available, how many hours do they have to work to finish the same job?
3.) At 65 km/hr, Alfred can reach home in 50 minutes. At what speed should he drive his car so that he can reach home 10 minutes earlier?
4.) A land area was divided among the three heirs in the ratio 5:2:4. If the largest share was 20 hectares of land, what is the total are of the land?
5.) A certain amount of money is divided among Rio, Kim and Leo in the ratio 5:7:3. If Leo gets Php 24,000.00, how much is the total amount?​

Answer 1

These problems illustrate how to use proportions, ratios, and unit rates to solve for unknown quantities in various scenarios such as distance, time, and allocation of shares. Each scenario involves setting up and solving a proportion to find the unknown value.

Step-by-step explanation:

The problems provided are examples of how to solve proportions using ratios and unit rates.

1. For the first problem, to determine how far a car can travel in 5 hours based on its speed over 3 hours, we use the ratio 210 km in 3 hours. This is a direct proportion since more hours will result in more kilometers traveled. We set up a proportion where the distance for 5 hours is the unknown (x), so 210 km / 3 hours = x km / 5 hours.
2. The second problem involves an inverse proportion because fewer people painting will take more time to finish the job. For 5 people taking 5 hours, we can write the ratio as 5 people / 5 hours. We then compare this to the situation with 2 people; 5 people / 5 hours = 2 people / x hours.
3. For Alfred to reach home 10 minutes earlier, we need to convert his usual travel time to minutes, create a ratio of distance to time, and solve for the new speed (unit rate).
4. The fourth problem involves a direct proportion between the ratio of land division (5:2:4) and the total land area. Since the largest share is 20 hectares, corresponding to the ratio part of 4, we set up a proportion to find the total area.
5. The fifth problem is similar to the fourth, where the money ratio (5:7:3) helps to determine the total amount based on Leo's share of Php 24,000, corresponding to the ratio part of 3.

It is important to set up the proportion correctly, compare the correct quantities, and then solve for the unknown variable. Checking that the answer is reasonable is also a critical step in problem-solving.