Final answer:
To find the speed at which Janice drove to the soccer game, an algebraic equation was set up using the distance-rate-time relationship. After setting up and solving the quadratic equation x^2 - 20x - 800 = 0, it was determined that Janice drove at 40 miles per hour to the soccer game.
Step-by-step explanation:
Janice went on a 40 mile trip to a soccer game and had to drive 20 miles per hour slower on the way back due to road construction, making the return trip take 1 hour longer. To solve for the speed at which she drove to the soccer game, we can set up an algebraic equation using the relation distance = rate × time. Let x represent the speed (rate) at which Janice drove to the soccer game, and x - 20 represent the speed on the way back.
The time taken to travel to the game is 40/x hours, and the time taken for the return trip is 40/(x - 20) hours. According to the information given, the return trip took 1 hour longer, so we have the equation 40/x + 1 = 40/(x - 20). To find x, we solve the equation:
- Multiply both sides by x(x - 20) to clear the denominators: 40(x - 20) + x(x - 20) = 40x.
- Expand the left side: 40x - 800 + x^2 - 20x = 40x.
- Simplify the equation: x^2 - 20x - 800 = 0.
- Factor the quadratic equation to solve for x.
- Ignoring the negative solution which doesn't make sense in this context, we find that Janice's speed to the game was 40 mph
Therefore, Janice drove 40 miles per hour to the soccer game.