Travel Math Question.......What if?

Question

If I travel 8 miles South and 6 miles Southeast and then 100 miles West at the speed of 20mph, and my friend is traveling 14 miles South and 94 miles West at the speed of 15 mph, then will we arrive at the same spot at the same time?

Answer 1

a) not at the same time: you cannot travel 114 miles at 20 MPH and 108 miles at 15 MPH in the same amount of time (the first would take 5.7 hours, the second 7.2 hours). However, the question doesn't say you both left at the same time, so...

b) you travel 8 miles south, then 6 miles SE, which is less than 14 miles south (more in the neighborhood of 11 miles south), while your friend travels 14 miles south, therefore it would be impossible for you both to end up at the same spot (you would travel 8 + sqrt18 miles south, or 12.25 miles south)

Answer 2

You will both not arrive at the same spot.
your travel path will take you to a spot 1.75 miles west and 1.74 miles north of where your friend will end up.

If both of you ended up at the same spot then:

114 miles @ 20 mph takes 5.7 hrs
108 miles @ 15 mph takes 7.2 hrs

Now, if both of you had left at the same time then you will get there 1.5 Hrs before your friend, the only way both of you will get there at the same time, if you ended up in the same spot, is if your friend gets a 1.5 Hr head start.

This is where your cell phones come in handy and you both will ask the most common question asked on cell calls "Where are you?"

Answer 3

(8+6+100)/20 ≠ (14+94)/15

Answer 4

your friend travel 14 miles south and then he turns west.
distance travelled by you southwards before turning west,
=8+6*cos45
=12.24(approx)
therefore you and your friend wiil never meet.

Answer 5

A big "No"