Speed Golf Cart
What is the average speed for the entire trip?
A golfer rides in a golf cart at a speed of 3.10 m/s for 20.0 s. She then gets out of the cart and starts walking at an average speed of 1.20 m/s. For how long (in seconds) must she walk if her average speed for the entire trip, riding and walking, is 2.60 m/s? ______s
In problems of this type, someone travels a distance d1 at a rate r1. Then they travel a distance d2 at a rate r2. The problem is to find the average rate. To solve such a problem, use the basic equation
Time = Distance/Rate
The times for the travel are
t1 = d1/r1 and t2 = d2/r2, so the total time is t1 + t2. The total distance is d1 + d2. Hence, the average rate (r) is total distance divided by total time,
r = (d1 + d2)/(d1/r1 + d2/r2)
This is our basic equation.
We know that r1 = 3.10 m/s and t1 = 20.0 s, so d1 = r1t1 = 62 m.
We know that r2 = 1.20 m/s and r = 2.60 m/s, so we need to find d2.
Plugging in to the basic equation gives
2.60 = (62 + d2)/(20 + d2/1.20)
62 + d2 = 2.60(20 + d2/1.20)
62 + d2 = 52 + 2.166666d2
10 = 1.1666666d2
d2 = 8.571428 m
Hence t2 = d2/r2 = 8.571428/1.2 = 7.142857 s.
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