A bicyclist travels the first 700 m of a trip at an average speed of 8 m/s, travels the next 600 m in 90 s and the last 50s at a speed of 21 m/s. Find the average speed of the bicyclist for this trip.

Question

anonymous · Answer

help me please

tanya123 · Answer

@iPwnBunnies @Kainui

anonymous · Answer

thank you tanya

ipwnbunnies · Answer

We want to find the speed of each segment of this trip, the time elapsed during each segment. Also we want to find the total time of the trip.

So, Segment 1: 700 m at 8 m/s. They give us the speed, we want time.
$$\frac{700 m}{8 \frac{m}{s}} = 87.5 s$$

ipwnbunnies · Answer

Segment 2: 600 m in 90 seconds. They give us time, we also need speed.
$$\frac{600 m}{90 \sec} = 6.67 \frac{m}{s}$$

ipwnbunnies · Answer

Segment 3: We're given both the speed and the time. 21 m/s at 50 seconds.

The main idea of average speed is the add up the "work" each speed did with respect to time.

$$Avg. speed = (8 \frac{m}{s})(\frac{87.5s}{227.5s} ) + (6.67 \frac{m}{s})(\frac{90s}{227.5s} )+(21 \frac{m}{s})(\frac{50s}{227.5s})$$

ipwnbunnies · Answer

For example, the first term. This represent the first segment of the race.
I put the speed the bicyclist was going, 8 m/s. I multiplied that by the fraction of time of the entire trip: the time of segment 1 divided by the total time.

Do that for every segment, then add up.