A cyclist traveled east at 15 meters per second for 15 seconds, and then he stopped to rest for 10 seconds. Then he moved west at two meters per second for 75 seconds. Find the cyclist’s average speed for the whole trip.
To find the average speed, we’ll first have to find the total distance our cyclist travelled and then the total time he was travelling for. Let’s see what information we’re given. We know the first segment, our cyclist was travelling 15 meters per second for 15 seconds. In the second segment, he stopped to rest for 10 seconds. And finally, he travelled at two meters per second for 75 seconds.
To find the total distance our cyclist travelled during the first part of his trip, we’ll need to multiply the speed he was travelling in it by how long he travelled. The speed he was travelling times the time he was travelling equals the distance. This will give us the distance of the first segment. In the first segment, he travelled 225 meters.
And our cyclist rested for 10 seconds. During his rest, he travelled zero meters because he wasn’t on his bike.
In the final portion, he travelled at two meters per second for 75 seconds. And again, we’ll need to multiply the speed times the time to get the distance. During the third portion, he travelled 150 meters.
Now that we know the distances travelled, we’ll need to add all of the distances he travelled together. 225 meters plus zero meters plus 150 meters.
For the denominator, we’ll need to know the time, the time that he travelled altogether. This requires the time that he took at each of the three segments. 15 seconds plus 10 seconds plus 75 seconds.
When you add up the distance travelled, it’s 375 meters. And the time he travelled, 100 seconds. He travelled 375 meters in 100 seconds. We wanna reduce this fraction so that we know how many meters he was travelling per second. Here, I’ll divide the numerator and the denominator by 100. When I do that, I get 3.75 meters per second.
Our cyclist’s average speed is 3.75 meters per second.