A cyclist was riding a bike

Question

1. A cyclist managed to ride 5 miles against the wind in the same time than it took him to ride 10 miles with the wind . If the wind speed is 4mph, which equation can be used to calculate the cyclists average rate of speed in mpg?
2. 
   
3. Answer choices

A.) (10/r+4)=(5/r-4)

B.) (5/r+4)=(10/r-4)

C.) 10r-4= 5r+4

D.) 10(r+4)= 5(r-4)

Answer 1

The answer is "None of the above."

Let r = rate of speed of the bike.

We know distance = rate * time. (d = rt)

Since the time it took riding with the wind is the same as riding against the wind...

t = d_w / (r + 4) = d_a / (r - 4) where d_w = distance ridden with the wind = 10, and

d_a = distance ridden against the wind = 5

10 / (r + 4) = 5 / (r - 4)

can also be written as

10 (r - 4) = 5 (r + 4)

Answers A & C above are close, but are missing parentheses.

The rate, r, of the bike is therefore 12 mph.

And the time, t, to ride the distance with the wind is 5/8 hour. And against the wind is also 5/8 hour.