a tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.0m/s. the car is a distance d away the bear is 26m behind the tourist and running at 6.0m/s. the tourist reaches the car safely what is the maximum possible value for d?
i got the answer, but the unit just doesnt match.
my way to do it is:
£¨26m)(6m/s-4m/s)=52 m^2/s
who can give me some hints?
thanks a lot!!!
bear distance= 26 +tourist distance
6*time=26 + 4*time solve for time.
time= 13 seconds
6*time= bear distance
To find the maximum possible value for d, we need to consider the time it takes for the tourist to reach the car before the bear catches up to them.
We know the tourist is running at a speed of 4.0 m/s and the bear is running at a speed of 6.0 m/s. The bear is initially 26 m behind the tourist, so the distance between the bear and the car is (d + 26) m.
The time it takes for the tourist to reach the car is given by:
Time = Distance / Speed
For the tourist: Time = d m / 4.0 m/s
For the bear: Time = (d + 26) m / 6.0 m/s
Since the tourist reaches the car safely, the time it takes for the tourist to reach the car must be less than or equal to the time it takes for the bear to reach the car.
So we can set up the following inequality:
d / 4.0 ≤ (d + 26) / 6.0
To solve this inequality, we can cross multiply and simplify:
6.0d ≤ 4.0(d + 26)
6.0d ≤ 4.0d + 104
2.0d ≤ 104
d ≤ 52
Therefore, the maximum possible value for d is 52 meters.