To solve this problem, we need to calculate when the second car will travel the same distance as the first car.

Step 1: Calculate the distance the first car travels each hour. This is easy because the first car travels at a constant speed of 10 km/h. So, in 't' hours, the first car will travel 10t km.

Step 2: Calculate the distance the second car travels each hour. This is a bit more complicated because the second car's speed increases each hour. In the first hour, it travels 8 km. In the second hour, it travels 8.5 km (because its speed increases by 0.5 km/h). In the third hour, it travels 9 km, and so on. So, in 't' hours, the second car will travel 8t + 0.5(t(t-1)/2) km. The term t(t-1)/2 represents the sum of the first 't' natural numbers, which is used here because the speed increases by 0.5 km/h each hour.

Step 3: Set the distances equal to each other and solve for 't'. This gives us the equation 10t = 8t + 0.5(t(t-1)/2). Simplifying this equation gives us t^2 - 19t = 0.

Step 4: Solve the quadratic equation. The solutions to this equation are t = 0 and t = 19. We can ignore t = 0 because it represents the starting time. So, the second car will overtake the first car after 19 hours.

So, none of the options given (9 hours, 7 hours, 8 hours, 5 hours) is correct. The correct answer should be 19 hours.

Question

To solve this problem, we need to calculate when the second car will travel the same distance as the first car.

Step 1: Calculate the distance the first car travels each hour. This is easy because the first car travels at a constant speed of 10 km/h. So, in 't' hours, the first car will travel 10t km.

Step 2: Calculate the distance the second car travels each hour. This is a bit more complicated because the second car's speed increases each hour. In the first hour, it travels 8 km. In the second hour, it travels 8.5 km (because its speed increases by 0.5 km/h). In the third hour, it travels 9 km, and so on. So, in 't' hours, the second car will travel 8t + 0.5(t(t-1)/2) km. The term t(t-1)/2 represents the sum of the first 't' natural numbers, which is used here because the speed increases by 0.5 km/h each hour.

Step 3: Set the distances equal to each other and solve for 't'. This gives us the equation 10t = 8t + 0.5(t(t-1)/2). Simplifying this equation gives us t^2 - 19t = 0.

Step 4: Solve the quadratic equation. The solutions to this equation are t = 0 and t = 19. We can ignore t = 0 because it represents the starting time. So, the second car will overtake the first car after 19 hours.

So, none of the options given (9 hours, 7 hours, 8 hours, 5 hours) is correct. The correct answer should be 19 hours.

Knowee AI · Accepted Answer

To solve this problem, we need to calculate when the second car will travel the same distance as the first car.

Step 1: Calculate the distance the first car travels each hour. This is easy because the first car travels at a constant speed of 10 km/h. So, in 't' hours, the first car will travel 10t km.

Step 2: Calculate the distance the second car travels each hour. This is a bit more complicated because the second car's speed increases each hour. In the first hour, it travels 8 km. In the second hour, it travels 8.5 km (because its speed increases by 0.5 km/h). In the third hour, it travels 9 km, and so on. So, in 't' hours, the second car will travel 8t + 0.5(t(t-1)/2) km. The term t(t-1)/2 represents the sum of the first 't' natural numbers, which is used here because the speed increases by 0.5 km/h each hour.

Step 3: Set the distances equal to each other and solve for 't'. This gives us the equation 10t = 8t + 0.5(t(t-1)/2). Simplifying this equation gives us t^2 - 19t = 0.

Step 4: Solve the quadratic equation. The solutions to this equation are t = 0 and t = 19. We can ignore t = 0 because it represents the starting time. So, the second car will overtake the first car after 19 hours.

So, none of the options given (9 hours, 7 hours, 8 hours, 5 hours) is correct. The correct answer should be 19 hours.

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