A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.04 m/s. The car is a distance d away. The bear is 17.5 m behind the tourist and running at 7.26 m/s. The tourist reaches the car safely. What is the maximum possible value for d?
time=d/5.04
time=(d+17.5)/7.26
set them equal, solve for d
How do you set them equal to d. I am having a lot of trouble doing this.
To find the maximum possible value for d, we need to determine the distance the bear would have traveled while the tourist reaches the car.
Let's first calculate the time it takes for the tourist to reach the car. We can use the formula:
Distance = Speed × Time
The distance the tourist needs to cover is "d", and the speed is given as 5.04 m/s. Therefore, the time taken by the tourist to reach the car is:
Time = Distance / Speed
= d / 5.04
Now, let's calculate the distance the bear would have traveled during that time. The bear is initially 17.5 m behind the tourist and runs at a speed of 7.26 m/s.
Distance traveled by bear = Speed × Time + Initial Distance
= 7.26 × Time + 17.5
Since we want to find the maximum possible value for d, the bear should be as close as possible to the tourist when the tourist reaches the car. In other words, when the bear reaches the closest distance to the tourist, the distance between them should be zero.
So, we want to find the value of d that satisfies the equation:
7.26 × Time + 17.5 = 0
We know that Time = d / 5.04, so we can substitute this into the equation:
7.26 × (d / 5.04) + 17.5 = 0
Simplifying the equation:
7.26d + 17.5 × 5.04 = 0
7.26d + 88.2 = 0
7.26d = -88.2
d = -88.2 / 7.26
Calculating this:
d ≈ -12.15
Since distance cannot be negative, we discard the negative value. Therefore, the maximum possible value for d, the distance between the car and the tourist, is approximately 12.15 meters.