SOLUTION: Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than Smith, and his trip took 1/2 hour longer than Smith's. How fast
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Question 62053: Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than Smith, and his trip took 1/2 hour longer than Smith's. How fast was each one traveling? Answer by uma(370) (Show Source):
You can put this solution on YOUR website! Let the speed of Smith be x mph
Then speed of Jones = (x+5) mph
Distance covered by Smith = 45 miles.
So time taken by Smith = Distance/time
= 45/x hrs
Distance covered by Jones = 70 miles.
Time taken by Jones = 70/(x+5) hrs.
By the given data,
70/(x+5) - 45/x = 1/2
Multiplying throughout by 2x(x+5) we get,
70*2x - 45*2(x+5) = x(x+5)
==> 140x - 90x - 450 = x^2 + 5x
==>50x - 450 - x^2 - 5x = 0
==> -x^2 + 45x - 450 = 0
==> x^2 - 45x + 450 = 0
==> x^2 - 15x - 30x + 450 = 0
==> x(x-15) - 30(x - 15) = 0
==> (x-15)(x-30) = 0
==> x-15 = 0 or x-30 = 0
==> x = 15 or x = 30
So either their speeds are 15 mph and 20 mph Or
their speeds are 30 mph and 35 mph respectively.
In either cases the difference in time taken = 1/2 hr.
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