SOLUTION: Two hikers, Juan and Pedro started from the same place at the same time towards Arayat which is 90 kilometers away from their place. Pedro traveled 1 kilometer per hour faster than

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Question 1170811: Two hikers, Juan and Pedro started from the same place at the same time towards Arayat which is 90 kilometers away from their place. Pedro traveled 1 kilometer per hour faster than Juan and reached Arayat 1 hour before him. Find the rate of each hiker
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two hikers, Juan and Pedro started from the same place at the same time towards Arayat which is 90 kilometers away from their place.
Pedro traveled 1 kilometer per hour faster than Juan and reached Arayat 1 hour before him.
Find the rate of each hiker
:
let j = Juan's hiking rate
then
(j+1) = Pedro's hiking rate
:
Write a time equation; time = dist/rate
:
J's time - P's time = 1 hr
90%2Fj - 90%2F%28%28j%2B1%29%29 = 1
multiply equation by j(j+1), cancel the denominators
90(j+1) - 90j = j(j+1)
90j + 90 - 90j = j^2 + j
arrange as quadratic equation
j^2 + j - 90 = 0
Factors to
(j+10)(j-9) = 0
The positive solution
j = 9 mph is J's hiking rate
then, obviously, 10 km/h is Pedro's
:
:
Check solution
90/9 - 90/10 =
10 - 9 = 1