SOLUTION: Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A and travels the same distance in 2 hours less. Find the speed of each.

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Question 1186764: Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A and travels the same distance in 2 hours less. Find the speed of each.
Found 3 solutions by Alan3354, ikleyn, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A and travels the same distance in 2 hours less. Find the speed of each.
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t = 60/r
t-2 = 60/(r+5)
----
(60/r) - 2 = 60/(r+5)
(60-2r)/r = 60/(r+5)
60r = (60-2r)*(r+5) = -2r^2 + 50r + 300
---
2r^2 - 10r - 300 = 0
r^2 - 5r = 60
r^2 - 5r + 6.25 = 66.25
(r-2.5)^2 = 66.25
r = sqrt(66.25) + 2.5
r =~ 10.6394 km/hr

Answer by ikleyn(52773)   (Show Source):
You can put this solution on YOUR website!
.
Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A
and travels the same distance in 2 hours less. Find the speed of each.
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            The solution by @Alan is incorrect.
            I came to bring you a correct solution.

Let x be the speed of cyclist A, in km/h. Then the speed of cyclist B is (x+5) km/h, according to the condition. Cyclist A spent hours. Cyclist B spent hours. The difference of times is 2 hours. It gives you THIS "time equation" - = 2. (1) At this point, I just can to guess the answer mentally : it is x= 10 km/h. But let's get it formally . . . From the time equation, by multiplying both sides by x*(x+5) you get 60(x+5) - 60x = 2x*(x+5) 60x + 300 - 60x = 2x^2 + 10x 300 = 2x^2 + 10x 2x^2 + 10x - 300 = 0 x^2 + 5x - 150 = 0 Factor left side (x-10)*(x+15) = 0 The last equation has two roots, 10 and -15, of which we select the positive value x= 10. ANSWER. Cyclists A speed is 10 km/h; Cyclist B speed is 10+5 = 15 km/h. CHECK. Calculate left side of the equation (1). It is - = 6 - 4 = 2 hours. ! Correct !

Solved.

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Couple of words as a conclusion.

What I presented here, is a standard version and a standard way solving such problems using "time equation".

It is straightforward and clear. It prevents you of making mistakes.

If you deviate from this scheme of writing the solution, and will write a mess, then NOTHING will prevent you
of making mistakes on the way.

Answer by MathTherapy(10551)   (Show Source):
You can put this solution on YOUR website!
Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A and travels the same distance in 2 hours less. Find the speed of each.

Let cyclist A's speed be S Then cyclist B's speed is: S + 5 We then get the following TIME equation: ------ Factoring out GCF, 2, in the numerator 30S + S(S + 5) = 30(S + 5) ------ Multiplying by LCD, S(S + 5) (S - 10)(S + 15) = 0 S - 10 = 0 OR S + 15 = 0_____S = - 15 (ignore)