A golfer rides in a golf cart at an average speed of 3.10 m/s for 28.0 s. She then gets out of the cart and starts walking at an average speed of 1.30 m/s. For how long (in seconds) must she walk if her average speed for the entire trip, riding and walking, is 2.10 m/s?
To solve this problem, we need to use the concept of average speed. Average speed is defined as the total distance traveled divided by the total time taken.
Let's assume that the golfer walks for time 't'. In the given scenario, she rides in a golf cart for 28.0 seconds and walks for 't' seconds.
The total distance traveled while riding the cart is given by:
Distance1 = Speed1 × Time1
Distance1 = 3.10 m/s × 28.0 s
The total distance traveled while walking is given by:
Distance2 = Speed2 × Time2
Distance2 = 1.30 m/s × t
Now, we have the total distance traveled and the total time taken. We can use this information to find the average speed of the entire trip.
Average speed = Total distance / Total time
Average speed = (Distance1 + Distance2) / (Time1 + Time2)
Substituting the given values:
2.10 m/s = (3.10 m/s × 28.0 s + 1.30 m/s × t) / (28.0 s + t)
Now, we can solve this equation to find the value of 't'.
First, let's cross multiply:
2.10 m/s * (28.0 s + t) = 3.10 m/s * 28.0 s + 1.30 m/s * t
Expanding the equation:
2.10 m/s * 28.0 s + 2.10 m/s * t = 3.10 m/s * 28.0 s + 1.30 m/s * t
Now, let's isolate 't' on one side:
2.10 m/s * t - 1.30 m/s * t = 3.10 m/s * 28.0 s - 2.10 m/s * 28.0 s
Simplifying the equation:
0.80 m/s * t = 1.00 m/s * 28.0 s
Finally, divide both sides by 0.80 m/s to solve for 't':
t = (1.00 m/s * 28.0 s) / 0.80 m/s
Calculating this, we find:
t = 35.0 s
Therefore, the golfer must walk for 35.0 seconds in order to have an average speed of 2.10 m/s for the entire trip.