Question 164004
Brenda and her husband Randy bicycled cross - country together. One morning,
 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, distance 30 mi
then
(s+5) = R's speed, distance 60 mi
:
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)
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s = 60s
:
Arrange as a quadratic equation:
s^2 + 5s + 30s - 60s + 150 = 0
:
s^2 - 25s + 150 = 0
Factors to:
(s - 10)(s - 15) = 0
:
s = 10 mph is B's speed, then R's speed = 15 mph
or
s = 15 mph is B's speed, then R's speed = 20 mph
:
If substitute either value for s you will find that it's true