aircraft used for fire spotting..

[droodles]

an aircraft, used for fire spotting flies from its base to locate a fire at an unknown distance, x km away. It travels straight to the fire and back averaging 240km/h for the outward trip and 320 km/h for the return. If the plane was away for 35 minutes, find the distance x km.

I don't understand how to setup the equation.

[unknown id]

set up two equations:

Let t = the time taken for the outward trip
Let T = the time taken for the inward trip

Thus,

t + T = 35/60 hours (1)

240t = 320T
=> 240t - 320T = 0 (2)

Then solve using simultaneous equations:

x = 240t or x = 320T

and u should get x = 80 km

[Mao]

240 km/h is 4 km/min
320 km/h is 16/3 km/min

since time=

hence:




lol droodles

[droodles]

a group of hikers is to travel x km by bus at an average speed of 48km/h to an unknown place. They then plan to walk back along the same route at 4.8km/h and to arrive 24 hours after setting out on the bus. If they allow 2 hrs for lunch, how far must the bus take them?

distance = x so it should be..

5x/4 + ...  = 1320mins (providing that its 22hrs x 60)

[unknown id]

One equation only needed this time:

Let x = the one-way distance of the trip

Thus,

x/4.8 + x/48 + 2 = 24
x = 96 km

[Mao]

john's free=dave free = T
john's goal= dave's goal = G

T + 2G= 11
T + 2(2G) = 19

2G=8
G=4
T=3

John's goals = G = 4
David's goals = 2G = 8

xD

EDIT: caramel i beat u to it!

[Collin Li]

Let Dg be the number of field goals by David
Let Dt be the number of free throws by David

Let Jg be the number of field goals by John
Let Jt be the number of free throws by John

19 = Dt + 2Dg (Dave scored 19)
11 = Jt + 2Jg (John scored 11)

Dt = Jt (David scored the same number of free throws as John)
Dg = 2Jg (...but twice as many field goals)

What do you want to find out? These equations are enough to solve the entire system.

[Collin Li]

I've noticed you're asking a lot of these types of questions. What you should do is assign variables to all the fundamental unknowns, like the number of field goals that each player is scoring, and then the number of free throws that each player is scoring.

Set up an equation with all the information you know, and you should always have enough information. If you have 'n' or more number of "linearly independent" equations and 'n' number of unknown variables, you always have enough information to solve the system.

Linearly independent means that they're not pretty much exactly the same, i.e.: 4A = 2B => 2A = B are not two different equations.