Brenda and her husband randy bicycled cross country together. ?

  • Thread starter Thread starter Kelly B
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Kelly B

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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?

I need to show my work...
 
Let x = speed of Brenda
x + 5 = speed of Randy
30/x = time of Brenda
1 + 30/x = time of Randy
(x + 5)(1 + 30/x) = 2(30) Randy covered twice the distance
(x + 5)(x + 30)/x = 60
x^2 + 35x + 150 = 60x
x^2 - 25x + 150 = 0
(x - 10)(x - 15) = 0
x = 10 or 15 mph Speed of Brenda
x = 15 or 20 mph Speed of Randy

There are two sets of answers
Speed of (Brenda, Randy) = (10, 15)
Speed of (Brenda, Randy) = (15, 20)
Each set of answer would satisfy the conditions.
 
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