Question

Ju-yi just got back from A 10 mile bicycle ride and she had ridden three miles per hour faster. The ride would have taken her 30 fewer minutes. What was her speed on the ride?

Answer 1

`6.39\ miles/hr`

Explanation:

`Let\ her\ speed=x\ mile/hr\\\\Let\ time\ taken=t\ hr\\\\distance=speed* time\\\\10=x* t\ .........................(1)`

When speed is 3 mi/hr faster.

`Her\ speed=x+3\ mile/hr\\\\Time\ taken=t-(1)/(2)\ hr\ \ \ as\ it\ takes 30\ minutes\ fewer\ and\ 30\ min=(1)/(2)\ hr\\\\distance=speed* time\\\\10=(x+3)* (t-(1)/(2))\\\\10=xt+3t-(x)/(2)-(3)/(2)\......................eq(2)\\\\eq(2)-eq(1)\\\\10-10=xt+3t-(x)/(2)-(3)/(2)-xt\\\\3t=(x)/(2)+(3)/(2)\\\\t=(x+3)/(6)\\\\from\ equation\ 1\ t=(10)/(x)\\\\(10)/(x)=(x+3)/(6)\\\\60=x^2+3x\ \ \ \ \ \ \ \ \ cross\ multiplication\\\\x^2+3x-60=0`

`Solution\ of\ ax^2+bx+c=0\ is\ given\ by\ x=(-b\pm√(b^2-4ac))/(2a)\\\\Here\ a=1,b=3\ and c=-60\\\\x=(-3\pm√(3^2-4* 1* (-60)))/(2)\\\\x=(-3\pm√(9+240))/(2)\\\\Only\ positive\ value\ will\ be\ taken\\\\x=(-3+√(9+240))/(2)=6.39\ miles/hr`