maths
posted by Tammy
A party of bush walkers have an average speed of 50km/minute and walk for 4 hours on a bearing of 231°T. they then walk for 6(1)/(3) hours on a bearing of 117°T. Find a.How far are they from bas e camp?
b. The bearing they must travel along to get to base camp

MathMate
I assume the speed of the adventurers are 50 m/min. since 50km/min is almost the speed of a supersonic jet.
Also, not clear about the 6(1)/(3) hours. I take it at face value of 2 hours.
The bearing of 231°T will be assumed to be measured from true north, clockwise, equivalent to "azimuth" used in US and French speaking countries.
The solution here lies in the resolution of all distances travelled to directions east (xaxis) and north (yaxis). The components can then be summed together to get the final destination and direction, if required.
There is a little problem combining bearings and trigonometry, the latter measures angles from zero in the east direction counter clockwise.
So to calculate sines and cosines using trigonometry, and with x≡East and Y≡North, we subtract the bearing from 90°.
For example, a bearing of 117° will be calculated as (90117)=27° in trigonometry.
Now we're ready to sum the distances:
The distances are:
1. 4*60*50=12000m
2. 2*60*50=6000m
Bearing Angle
231°T > 90231=141°
117°T > 90117=27°
leg Distance(D) Angle(A) Dcos(A) Dsin(A)
1 12000 141° 9325.75 7551.84
2 6000 27° 5346.04 2723.94
Sum (x2,y2)=(3979.71,10275.78)
Distance = sqrt(x2²+y2²)
angle
= arctan(10275.78/3979.71)
Note that since both numbers are negative, angle is in 3rd quadrant
= 248.83°(trig.)
convert to bearing, subtract from 90 and add 360 if result is negative
= (90248.83)+360
= 201.17°T
Check all calculations please. 
Tammy
Thank you so much for all your help you my friend are a legend! Sorry about the mistakes :0
Respond to this Question
Similar Questions

Math
a plane flies 1.5 hours at 110 mph on a bearing of 10°. it then turns and flies 8.5 hours at the same speed on a bearing of 100°. How far is the plane from its starting point? 
Maths
Two nomads leave camp at the same time.one walks at 5km/h on a bearing 039 degree.the other walks at 7.5km/h on a bearing 265 degree.after 2 hours how far apart are they and what is the bearing of the second from the first? 
Maths
Two normads leaves camp at the same time,one walks 5km/h on a bearing of 39 degree and the other walks 7.5km/h on a bearing of 265 degree after 2 hours.how far are apart and what is the bearing of the second from the first? 
Math
Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided … 
Math(DifferentQuestion,SameDescription)
Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided … 
Math(PleaseHelp, NewEquation SameDescription)
Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided … 
Vectors
A fishing boat leaves port at 8 miles per hour at a bearing of 220∘ for 5 hours, then turns to a bearing of 270∘ at 11 miles per hour for 4 hours, and finally changes to a bearing of 300∘ at 9 miles per hour for 4 hours. At this … 
Math, Precalc
A fishing boat leaves port at 4 miles per hour at a bearing of 80∘ for 3 hours, then turns to a bearing of 0∘ at 3 miles per hour for 4 hours, and finally changes to a bearing of 200∘ at 6 miles per hour for 5 hours. At this … 
math  trigonometry
A bushwalking party leave P and walk on a bearing of 335(degrees) for 11.4km until they reach Q. From Q they walk on a bearing of 65(degrees) for 18.7km at which point they arrive at R. a) What is the distance between R and P to 3 … 
math  bearings
Starting from their base in the national park, a group of bushwalkers travel 1.5 km at a true bearing of 030°, then 3.5 km at a true bearing of 160°, and then 6.25 km at a true bearing of 300°. How far, and at what true bearing, …