Question

Rosa went to a conference in a city 120km away. On the way back, due to road construction, he had to drive 10(km)/(hr) slower, which resulted in the return trip taking 2 hours longer. How past did he drive on the way to the conference?

Answer 1

Rosa drove at a speed of 30 km/hr to the conference.

Step-by-step explanation:

To solve this problem, let's set up equations based on the given information. Let x be the speed at which Rosa drove to the conference. The time it took Rosa to get to the conference can be calculated as 120km divided by x km/hr. On the way back, Rosa drove 10 km/hr slower, so the speed would be (x - 10) km/hr. The time it took Rosa to return is 120km divided by (x - 10) km/hr. We are told that the return trip took 2 hours longer, so we can set up the equation:

120km/(x -10) = 120km/x + 2

To solve this equation, we can multiply both sides by (x - 10) and x to eliminate the denominators.

120km * x = 120km * (x - 10) + 2 * x * (x - 10)

Simplifying the equation:

120x = 120x - 1200 + 2x^2 - 20x

Combining like terms:

0 = 2x^2 - 20x - 1200

Now we can solve this quadratic equation for x. We can either factor it or use the quadratic formula. Let's use the quadratic formula

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values a = 2, b = -20, and c = -1200:

x = (-(-20) ± √((-20)^2 - 4 * 2 * -1200)) / (2 * 2)

Simplifying:

x = (20 ± √(400 + 9600)) / 4

x = (20 ± √10000) / 4

x = (20 ± 100) / 4

There are two possible solutions:

x = (20 + 100) / 4 = 120 / 4 = 30

x = (20 - 100) / 4 = -80 / 4 = -20

Since speed cannot be negative, we can discard -20 km/hr as a solution. Therefore, Rosa drove at a speed of 30 km/hr to the conference.