You are on a limited budget and planning a four day camping trip to a national park. bus fare is 75 dollars each way and the ride takes 12 hours. plane fare is 150 dollars each way and and the ride takes an hour and a half. conduct a cost-benefit analysis to you choose your method of travel.

Considering that you are planning the trip with limited budget and only for 4 days (=96h) you must value both time and money when doing it.

If you use the bus you spend $75 + $75=$150 and 12h + 12h = 24h. This means you spend $150 to enjoy 96h - 24h = 72h of actually camping. This means you pay $150/72h = $2,08 per hour of actual camping.

On the other hand if you choose the plane you spend $150 + $ 150 = $300 and 1,5h + 1,5h = 3h. This means you spend $300 to enjoy 96h - 3h = 93h. This means you pay $300/93h = $3,22 per hour of actual camping.

Considering all that, taking the bus his the most cost-effective option (and the cheaper one also).

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west