Question

Riding with the wind at her back, a cyclist takes an hour less time to cover 80 miles than without any wind. Riding with the wind increases the cyclist's speed by 2 miles per hour. What is her speed when riding with the wind?

Answer 1

41 MPH

Explanation:

Let's assume the original speed with or without, is around 82 miles, within 2 hours.

So in this case, it'd be half the miles, half the hours!

Answer 2

Let the speed of cyclist without any wind = x miles per hour

Speed of cyclist when speed of wind increases by 2 miles per hour = (x + 2 )miles per hour

Also , relation that is given between speed of cyclist without wind and with wind is :Riding with the wind at her back, a cyclist takes an hour less time to cover 80 miles than without any wind.

Converting this statement into terms of equation:

`(80)/(x)-(80)/(x+2)=1  \\\\ 160 = x^2 + 2x \\\\ x^2 + 2x - 160=0 \\\\ x= (-2\pm√(4+640))/(2), {\text {As speed can't be negative, so taking positive value of x}} Gives,  x =11.68`→→→To solve the Quadratic equation of type : a x² + b x + c=0, I have used discriminant method, to find the roots, which is x=
`(-b\pm√(D=b^2-4ac))/(2a)`

Speed of cyclist without wind = 11.68 miles per hour

Speed of cyclist when wind is flowing = 11.68 +2 = 13.68 miles per hour