porportion word problems.

[csolinsky]

I have difficulty setting up these type of problems... no problem solving once set up.

Joe cycled 45 miles and john cycled 70 miles. John averaged 5 miles an hour more than Joe and his trip took 30 minutes longer. How fast was each travelling.

distance = 45 rate = x time =
distance = 70 rate = x + 30

t= d/r
t = 70/45 - x +30/x ????

Help

 

[jonboy]

Joe cycled 45 miles and john cycled 70 miles.

This is the distance cycled, not the speed or rate.

So you should have:

\(\displaystyle \L \;\;45\,=\,r(x\,+\,30)\)
\(\displaystyle \L \;\;70\,=\,(r\,+\,5)x\)

Solve for \(\displaystyle r\).

 

[Denis]

Joe @ x mph: ...........45.............> h hours
hx = 45 ; h = 45/x [1]

John @ (x+5) mph: .......................70.........................> (h + 1/2) hours
(h + 1/2)(x + 5) = 70 [2]

Simplify [2], then substitute [1] :
you'll get a quadratic, and 2 valid solutions.