SOLUTION: in canada, medicine and cranbrook are 300Km apart. Harry rides 20 Km per hr faster than yoshi rides his yamaha. find harry's average speed if he travels from cranbrook to medicine

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Question 200417This question is from textbook
: in canada, medicine and cranbrook are 300Km apart. Harry rides 20 Km per hr faster than yoshi rides his yamaha. find harry's average speed if he travels from cranbrook to medicine hat in 1.1/4 less time than yoshi. This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In Canada, Medicine Hat and Cranbrook are 300Km apart. Harry rides 20 Km per
hr faster than Yoshi rides his Yamaha. Find Harry's average speed if he
travels from Cranbrook to Medicine hat in 1.1/4 less time than Yoshi.
:
Let s = H's speed
then
(s-20) = Y's speed
:
Write a time equation; Time = dist%2Fspeed
H's time + 1.25 hrs = Y's time
300%2Fs + 1.25 = 300%2F%28%28s-20%29%29
Multiply equation by s(s-20), results:
300(s-20) + 1.25s(s-20) = 300s
:
300s - 6000 + 1.25s^2 - 25s = 300s
Arrange as a quadratic equation
1.25s^2 + 300s - 300s - 25s - 6000 = 0
:
1.25s^2 - 25s - 6000 = 0
Divide equation by 1.25 to simplify:
s^2 - 20s - 4800 = 0
Factor
(s - 80)(s + 60) = 0
The positive solution
s = 80 km/hr is H's average speed
:
:
Check solution by finding the times; (60 km/hr is Y's speed)
300/60 = 5 hrs
300/80 = 3.75 hrs
---------------
differ = 1.25 hr