Problema Solution
Brenda and rany bicycled cross-country together. One morning Brenda rode 30 minutes. By traveling only 5mph faster and putting in one more hour randy covered twice the distance Brenda covered. What was the speed of each cyclist?
Answer provided by our tutors
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 =
:
B's time + 1 hr = R's time
+ 1 =
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
+ 1 =
and
+ 1 =