Question

Starting at 48th Street, Dylan rides his bike due east on Meridian Road with the wind at his back. He rides for 20 min at 15 mph. He then stops for 5 min, turns around, and rides back to 48th Street; because of the headwind, his speed is only 10 mph.

Answer 1

Dylan's bike ride involves displacement and average velocity. He ends up back at the starting point after riding a certain distance and direction with the wind and then against the wind, resulting in a final displacement of zero miles.

Step-by-step explanation:

This question involves the concept of displacement and average velocity.

Dylan rides his bike east for 20 minutes at a speed of 15 mph. The distance he travels can be calculated by multiplying the speed by the time: (15 mph) x (20 min) = 300 miles. Since he rides in a straight line, his displacement is also 300 miles east.

After turning around and riding back, Dylan travels at a speed of 10 mph. In the opposite direction, his displacement will be the negative value of his initial displacement: -300 miles.

Overall, his final displacement is the sum of his initial displacement and his opposite displacement: 300 miles + (-300 miles) = 0 miles. This means that Dylan ends up back at the starting point, 48th Street.

Answer 2

55 min

Step-by-step explanation:

The missing question is: how long does the trip take?

First of all, we need to find the initial distance covered by Dylan. In the first part, he rides for

`t_1 = 20 min = (1)/(3)h`

at a speed of

v = 15 mph

therefore, the distance he covered is

`d = v t_1 = (15)((1)/(3))=5 mi`

Then Dylan stopped for a time of

`t_2 = 5 min = (5)/(60)=(1)/(12)h`

Finally, on the way back, Dylan covered again this distance but travelling at a new speed of

v = 10 mph

So, the time he took is

`t_3 = (d)/(v)=(5)/(10)=(1)/(2)h = 30 min`

So, the total time of the trip was

`t=t_1 + t_2 + t_3 = 20 min + 5 min + 30 min = 55 min`