Algebra Homework Help? Please show steps to solve this, so i can learn too. Thx*?

Question

[Formula: rt = d] A long distance cyclist pedaling at a steady rate travels 30 miles with the wind. He can travel only 18 miles against the wind in the same amount of time. If the rate of the wind 3 mph, what is the cyclist's rate without the wind?

Answer 1

r(x)+3(x)=30
r(x)-3(x)=18
6(x)=12
x=2

2r+3(2)=30
2r=24
r=12

Answer 2

Assuming the road is flat then wind resistance is basically all the cyclist has to overcome. We assume the cyclist can always go at the same speed relative to the wind.

Call the cyclist's speed relative to the wind "R" and the time he is underway (the same in both instances) "T"

Then we can write:

(R-3)T = 18 and
(R+3)T = 30

From the first of these equations we have T = 18/(R-3) and substituting this value for T in the second equation we get:

(R+3)/(R-3) x 18 = 30

therefore :
18R+54 = 30R-90 or simplifying, 12R = 144

Hence R = 12

This is the speed which the cyclist can ride relative to the wind and is therefore also his speed without wind.

I hope this is clear. Basically we have 2 unknowns here (R & T) so we need to have two independent equations to solve for these two unknowns. The conditions given enable us to write these two equations and achieve a solution.

Answer 3

The wind adds 3 mph to the bicyclist going with the wind and subtracts 3 mph to the bicylists going against the wind. Let x= speed without wind
With the wind 30 = x+3 x t
Against wind 18 = x-3 x t
Solve each for t and combine to get
30/(x+3) = 18/(x-3)
Cross multiply and rearrange to get
30x-90 = 18x+54 => 12x=144 and x=12 mph
The bicyclist goes 15 mph with the wind (2 hours)
The bicyclist goes 9 mph against the wind (2 hours)

Answer 4

let the speed of the cyclist is Rc miles/hour and the time taken to cover 30 miles is t and speed of wind is given as 3mph

Rc t=30 miles -----------(1)
against wind he will travel the distence
(Rc-3) *t = 18------------(2)
solve the above two equations as below

Rc t = 30
Rc t- 3t=18

3t=12
t= 4
Subsitute value of t in equation --1

Rc * 4 = 30
Rc = 30/4 = 7 1/2

ans Rc is 7 1/2 mph

Answer 5

30+18=48
48/2=24
30-18=12
12/2=6
3 is half of 6
biker rode for 2 hours
average distance covered=24
speed is 12 MPH

Answer 6

ahha another procrastinator thats like 7 so far this night