Can u help me solve this.?

Question

i've tried to solve it but im not sure of my answer.

A cyclist rode 6miles in 30 minutes with the wind and returned in 45 minutes riding against the wind. What is the average speed of the cyclist, and what is the wind speed?

Answer 1

let speed of cyclist - x miles/ hr
and wind -y miles/ hr

speed = dist /time

case 1 : Going in direction of wind (speed is added)
x+y = 6 / (1/2) = 12 ( 30 mins = 1/2 hrs)
case2:
x -y = 6 / (3/4) = 8 ( 45 mins = 3/4hrs )

solving 1 and 2
2x = 20
x =10

so y = 2

speed of cyclist = 10 miles / hr
speed of wind = 2 miles / hr

Answer 2

"A cyclist rode 6miles in 30 minutes with the wind..."

Calculate the cyclist's speed with the wind:
"6 miles in 30 minutes" = (6 miles)/(30 minutes)

Convert those minutes into hour or hours to get mph:
[(6 miles)/(30 minutes)] * [(60 minutes)/(1 hour)] = (6*60 miles) / (30*1 hour) = 12 mph


"...and returned in 45 minutes riding against the wind."
Let's assume he returns to the original point, but this time taking 45 minutes to go back 6 miles because he's going against the wind.

Convert that 6 miles in 45 minutes to mph:
[(6 miles) / (45 minutes)] * [(60 minutes) / (1 hour)] = 6*60/45 mph = 6*4/3 mph = 8 mph


Now, add those two speeds and divide it by 2: (12mph + 8mph)/2 = 10mph
This would be the average speed of the cyclist.

Now, compare this average speed individually with the cyclist's speed when riding with the wind, when riding against it. You'll see their common difference is 2mph. This is the wind speed.

Answer 3

The average speed of the cyclist is the total distance divided by the total time.
Average Rate = D/T
Avg. Rate= 12 miles/ 75 minutes
Avg Rate = 0.16 mile/minute
Avg Rate = 0.16 miles/minute x 60 minutes/hour
Avg Rate = 9.6 miles/hour

Riding with the wind 6miles in 30 minutes
Rate =D/T Rate = 6miles/30 minutes 0.2 miles per minute or multiply by 60 minutes/hour you get a speed of 12 miles per hour.

Riding Against the wind 6miles/45 minutes
Rate = 6/45 = 0.133 miles/minute
Rate = 0.133 x 60 = 8 miles/hour

If the difference in rates is due to the wind then
the time difference is 15 minutes over 6 miles
6 miles/15 minutes = 0.4 miles/minute or
0.4 miles/minute x 60 minutes/hour = 24 miles/hour
The wind speed is 24 miles/hour

Answer 4

Distance = Speed * Time
Speed = CyclistSpeed + TailWindSpeed

Going 6 miles = (CyclistSpeed + TailWindSpeed) * 30 minutes
Returning 6 miles = (Cyclist Speed - TailWindSpeed) * 45 minutes

(CyclistSpeed + TailWindSpeed) * 30 minutes = (CyclistSpeed - TailWindSpeed) * 45 minutes

(30 * CyclistSpeed) + (30 * TailWindSpeed) = (45 * CyclistSpeed - 45 * TailWindSpeed)

75 * TailWindSpeed = 15 * CyclistSpeed
5 * TailWindSpeed = CyclistSpeed

Going 6 miles = (CyclistSpeed + TailWindSpeed) * 30 minutes
6 miles = (5 * TailWindSpeed + TailWindSpeed) * 30 minutes
6 miles = 6 * TailWindSpeed * 30 minutes
1 mile / 30 minutes = TailWindSpeed
2 miles/hour = TailWindSpeed

5 * TailWindSpeed = CyclistSpeed
5 * 2 miles/hour = CyclistSpeed
10 miles/hour = CyclistSpeed

Answer 5

Let the speed of the cyclist be x mph and the speed of the wind be y mph
By the problem,
x+y=6/(1/2)=12 ...(1 ) [speed=distance/time]
x-y=6/(3/4)= 8 ....( 2) [45 minutes=3/4 hr]
adding we get,
2x=20
=.x=20/2=10
Subtracting 2 from 1 ,we get
2y=4
=>y=2
Therefore.the speed of the cyclist is 8 mph and that of the wind is 2 mph

Answer 6

the distant traveled by the cyclist is 12 mile
total time = 45 + 30 = 75 minutes
average speed = 12 mile / 75 min
which equal to 9.6 mile per hour

but your question about wind speed is very strange and make no sense because it depends on a lot of things like the surface of the cyclist which face the wind and a lot more of things

Answer 7

Let the speed of the cyclist be C and that of the wind be W(in miles per minute)
Thus, (C + W)x30=6 and
(C - W)x45=6.

3x(C + W)x30=3x6 or 90C +90W=18
2x(C-W)x45=2x6 or 90C -90W= 12

adding the above two, we get 180C=30. So, C=30/180=1/6 miles per minute or 10 miles per hour
Solving for W we get, 90x1/6+90W=18 or 15+90W=18
Thus,90W=3 i.e. W=3/90=1/30 miles per minute or 2 miles per hour.

Answer 8

let r = the rider's speed
let w = wind speed

6/(r + w) = 30/60
6/(r - w) = 45/60
r + w = 12
r - w = 8
2r = 20
r = 10 mph
w = 2 mph

Answer 9

v=d/t
v(go)=v(bike)+v(wind)=6/.5=12mph
that is going, now coming back
v(back)=v(bike)-v(wind)=6/.75=8mph
v(ave)=.5(v(go)+v(back))=20/2=10mph
that would make the wind speed the difference
v(go)-v(ave)=v(ave)-v(back)=2mph