Question 167686
 Brenda rode 30 miles. By traveling only 5 miles per hour faster and putting in
 one more hour, Randy covered twice the distance Brenda covered.
 What was the speed of each cyclist?
:
Let s = B's speed
then
(s+5) = R's speed
:
B traveled 30 mi
R traveled 60 mi (twice B's distance)
:
Write a time equation: Time = {{{distance/speed}}}
:
B's time + 1 hr = R's time
{{{30/s}}} + 1 = {{{60/((s+5))}}}
Multiply equation by s(s+5); results:
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s - 60s = 0
:
s^2 - 25s + 150 = 0; our old friend, the quadratic equation!
Factor:
(s - 15))(x - 10) = 0
:
both solutions will work:
s = 10 mph is B's speed, obviously, 15 mph = R's speed
and
s = 15 mph is B's speed, then 20 mph = R's speed
:

:
Check both solutions in the time equation
{{{30/10}}} + 1 = {{{60/15}}}
and
{{{30/15}}} + 1 = {{{60/20}}}