A golfer rides in a golf cart at an average speed of 3.10 m/s for 29.0 s. She then gets out of the cart and starts walking at an average speed of 1.40 m/s. For how long (in seconds) must she walk if her average speed for the entire trip, riding and walking, is 2.20 m/s?
avg speed= distance/total time
distance=3.1*29 m+1.4*t
2.20=(3.1*29+1.4t)/(29+t)
solve for t.
To solve this problem, we need to consider the distance covered while riding and walking, as well as the total time taken.
Let's start by calculating the distance covered while riding in the golf cart. We know that the average speed of the golfer in the cart is 3.10 m/s and the time spent riding is 29.0 s. We can use the formula:
Distance = Speed × Time
So, the distance covered while riding is:
Distance_riding = 3.10 m/s × 29.0 s
Now, let's calculate the distance covered while walking. We know that the average speed of the golfer while walking is 1.40 m/s. Let's denote the time spent walking as t (in seconds). The distance covered while walking is:
Distance_walking = 1.40 m/s × t
To find the total distance covered, we sum the distances covered while riding and walking:
Total distance = Distance_riding + Distance_walking
We also know that the average speed for the entire trip is 2.20 m/s. We can use the formula:
Average speed = Total distance / Total time
Therefore, we can write the equation as:
2.20 m/s = (Distance_riding + Distance_walking) / Total time
Substituting the values we already calculated, we have:
2.20 m/s = (3.10 m/s × 29.0 s + 1.40 m/s × t) / (29.0 s + t)
We can now solve this equation to find the value of t, which represents the time spent walking.
First, cross-multiply the equation:
2.20 m/s × (29.0 s + t) = 3.10 m/s × 29.0 s + 1.40 m/s × t
Distribute the multiplication:
2.20 m/s × 29.0 s + 2.20 m/s × t = 3.10 m/s × 29.0 s + 1.40 m/s × t
Multiply the values:
63.8 m + 2.20 m/s × t = 89.9 m + 1.40 m/s × t
Rearranging the equation to isolate t:
2.20 m/s × t - 1.40 m/s × t = 89.9 m - 63.8 m
0.80 m/s × t = 26.1 m
Finally, divide both sides by 0.80 m/s:
t = 26.1 m / 0.80 m/s
t ≈ 32.6 s
Therefore, the golfer must walk for approximately 32.6 seconds in order to have an average speed of 2.20 m/s for the entire trip.