Hi! I was solving this problem and then stopped because I didn't know how to solve it. Someone please help asap.

Question

Two boats leave the same dock at the same time, one travelling due west at 9 miles per hour and the other due north at 15 miles per hour. How many miles apart are the boats after three hours?

Answer 1

https://www.loom.com/share/4e116c82f2ff4505944e04a755fb4858

Hi there,

I've attached a video of me solving this problem, however, the sound didn't record! Apologies for this. The work is all there though, so I'll write up a little description of what I've done:

1) Draw a diagram to show the movement and direction of the two boats. Notice they are going in opposite directions at a right angle, and the distance between them forms a right triangle. This will be useful later.

2) Work out how far each boat has traveled after three hours. Each of them goes at a different rate, 9mph and 15 mph. To find out how far each goes, multiply their rate by the number of hours traveled.

3) I drew a new diagram with the new values which again shows a right triangle with a missing hypotenuse (longest side). Using the Pythagorean theorem, you can work out the hypotenuse as seen.

Let me know if you have any questions!

Answer 2

Hello Hansa;

Their positions eventually make up a right triangle as they move perpendicularly wrt each other.

The first one is at position 9 x 3 = 27m (West)

The second one is at position 15 x 3 = 45m (North)

The hypotenuse of the triangle formed there constitutes the distance between them.

D² = 27² + 45²

D = 729 + 2025

D = 52.478567 ~ 52.5 m

Answer 3

d = √(27² + 45²) = 52.48 mi