Studdy AI Logo
Math

QuestionYou hike 4 miles east and 2 miles north, then return. How far do you hike? Also, calculate your friend's hike via the well.

Studdy Solution

STEP 1

Assumptions1. The waterfall is4 miles east of the bikes. . The lookout point is miles north of the bikes.
3. The wishing well is3 miles north and miles west of the lookout point.
4. You and your friend travel along straight paths.

STEP 2

First, we need to find out how far you hike. You hike from the bikes to the waterfall, then to the lookout point, and finally back to the bikes. We can find the total distance by adding up these three distances.
Total distance=Distance to waterfall+Distance to lookout point+Distance back to bikesTotal\, distance = Distance\, to\, waterfall + Distance\, to\, lookout\, point + Distance\, back\, to\, bikes

STEP 3

Now, plug in the given values for the distances to the waterfall, to the lookout point, and back to the bikes to calculate the total distance.
Total distance= miles+2 miles+2 milesTotal\, distance =\, miles +2\, miles +2\, miles

STEP 4

Calculate the total distance you hike.
Total distance=4 miles+2 miles+2 miles=8 milesTotal\, distance =4\, miles +2\, miles +2\, miles =8\, miles

STEP 5

Next, we need to find out how far your friend hikes. Your friend hikes from the waterfall to the wishing well, then to the lookout point, and finally back to the bikes. We can find the total distance by adding up these three distances.
Total distance=Distance to wishing well+Distance to lookout point+Distance back to bikesTotal\, distance = Distance\, to\, wishing\, well + Distance\, to\, lookout\, point + Distance\, back\, to\, bikes

STEP 6

The distance to the wishing well from the waterfall is not directly given. However, we know that the wishing well is3 miles north and2 miles west of the lookout point. Since the lookout point is2 miles north of the bikes, and the waterfall is4 miles east of the bikes, we can use the Pythagorean theorem to find the distance from the waterfall to the wishing well.
Distance to wishing well=(Distance north)2+(Distance west)2Distance\, to\, wishing\, well = \sqrt{(Distance\, north)^2 + (Distance\, west)^2}

STEP 7

Now, plug in the given values for the distances north and west to calculate the distance to the wishing well.
Distance to wishing well=(3 miles)2+(2 miles)2Distance\, to\, wishing\, well = \sqrt{(3\, miles)^2 + (2\, miles)^2}

STEP 8

Calculate the distance to the wishing well.
Distance to wishing well=(3 miles)2+(2 miles)2= miles2+4 miles2=13 miles2=13 milesDistance\, to\, wishing\, well = \sqrt{(3\, miles)^2 + (2\, miles)^2} = \sqrt{\, miles^2 +4\, miles^2} = \sqrt{13\, miles^2} = \sqrt{13}\, miles

STEP 9

Now, plug in the calculated value for the distance to the wishing well, and the given values for the distances to the lookout point and back to the bikes to calculate the total distance your friend hikes.
Total distance=13 miles+2 miles+2 milesTotal\, distance = \sqrt{13}\, miles +2\, miles +2\, miles

STEP 10

Calculate the total distance your friend hikes.
Total distance=13 miles+2 miles+2 miles=13+4 milesTotal\, distance = \sqrt{13}\, miles +2\, miles +2\, miles = \sqrt{13} +4\, milesYou hike about8 miles, and your friend hikes about 13+4\sqrt{13} +4 miles.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord