SOLUTION: harry takes 2 hours less to travel 50 km than cara takes to travel 35 km. cara travels at a speed that is 5km/hr slower than that of harry. find the time taken by harry and cara to

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Question 683982: harry takes 2 hours less to travel 50 km than cara takes to travel 35 km. cara travels at a speed that is 5km/hr slower than that of harry. find the time taken by harry and cara to complete their respective journeys and the speed at which they traveled.
Answer by mananth(16946) (Show Source):
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Harry speed =x km/h
Harry distance = 50 km
Cara speed = x-5
Cara distance = 35 km
Time = d/r
Time taken by cara - time taken by Harry = 2
35/(x-5) - 50/x= 2
LCD = x(x-5)
multiply equation by x(x-5)
35x-50(x-5)=2x(x-5)
35x-50x+250=2x^2-10x
2x^2-10x+50x-35x-250=0
2x^2+5x-250=0
2x^2-20x+25x-250=0
2x(x-10)+25(x-10)=0
(x-10)(2x+25)=0
x=10 OR -12.5
speed cannot be negative
so x= 10 Harry's speed
Cara's speed = 10-5 = 5 km/h
time = d/r
50/10 = 5 hours time taken by Harry
35/(10-5)= 7 hours Time taken by Cara