Question

Please help!!!!


Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in a square grid (see map). They are both standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30 mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the corner of 10th avenue and E street.

Answer 1

The question is incomplete. Here is the complete question.

Doug is a dog and his friend Bert is a bird. They li in Slat Lake City, where the streets are 1/16 miles apart and arranged in a square grid (see map in the first attachment). They areboth standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20mi/hr. They are about to race to the corner of 10th avenue and E street.

a. Who do you predict will win, and why?

b. Draw the likely paths that Doug and Bert will travel.

c. What will you compare to determine the winner?

d. Devise a plan to calculate these, without measuring anything.

e. Who will win the race?

Answer: a. Bert will win the race; b. The drawing is in the second attachment; c. The time it will take for them to reach their destiny; d. Pythagorean Theorem; e. Doug wins the race.

Step-by-step explanation:

a. Bert could win the race because, as he can fly, his path towards the corner of 10th avenue and E street is a straight line, differently from Doug's path, which is composed by direction: 7 blocks west and 4 blocks north.

c. As their paths and speeds are different, it would be easier to compare the time they spent to reach the destination and, depending on the lesser time, determine who won.

d. To calculate the time, given the speed, it is needed to know the distance each one of them has traveled, since: speed = $\frac{distance}{time}$

Looking into the map, is easy to determine the distance Doug traveled.

For Bert, supossing he flied in a straight line from the beginning of the race to the end, it can be used Pythagorean Theorem (hypotenuse = $\sqrt{side^{2} + side^{2} }$) to determine the distance Bert traveled.

After finding the distance, time is determined as:

time = $\frac{distance}{speed}$

e. Time for Doug

distance = 7 blocks W + 4 bolcks N = 11 blocks

1 block id 1/16 miles apart, so:

d = 11*1/16 = 11/16 miles

time = $\frac{\frac{11}{16} }{30}$

time = $\frac{11}{16}$ . $\frac{1}{30}$

time = 0.023 hr

or

time = 0.023.60

time = 1.38 min

Time for Bert

distance = $\sqrt{7^{2} + 4^{2} }$

distance = $\sqrt{65}$

distance = 8.06225 blocks

distance = $\frac{8.06225}{16}$

time = $\frac{8.06225}{16}$. $\frac{1}{20}$

time = 0.025 hr

or

time = 0.025.60

time = 1.5 min

So, since Doug's time is less than Bert's time, Doug wins the race