SOLUTION: Two town A and B are 300 km apart. C is exacly halfway between A and B. A cyclist departs from B to C at x km/h at 9h00 and one hour later a second cyclist depatrs form A to C, 5 k

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Question 446486: Two town A and B are 300 km apart. C is exacly halfway between A and B. A cyclist departs from B to C at x km/h at 9h00 and one hour later a second cyclist depatrs form A to C, 5 km/h faster than the first cyclist. They reach C simultaneously.
1.1) Calculate, in terms of x, the time each cyclist requires to reach C.
1.2) Calculate at what time they will reach C.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two town A and B are 300 km apart. C is exacly halfway between A and B.
A cyclist departs from B to C at x km/h at 9h00 and one hour later a second
cyclist departs form A to C, 5 km/h faster than the first cyclist.
They reach C simultaneously.
:
1.1) Calculate, in terms of x, the time each cyclist requires to reach C.
Time = dist/speed
A cyclist: t(x) = 150%2Fx hrs
B cyclist: t(x) = 150%2F%28%28x%2B5%29%29 hrs
:
Find x
B's time + 1 hr = A's time
150%2F%28%28x%2B5%29%29 + 1 = 150%2Fx
:
Multiply by x(x+5), results:
150x + x(x+5) = 150(x+5)
150x + x^2 + 5x = 150x + 750
x^2 + 5x + 150x - 150x - 750 = 0
x^2 + 5x - 750 = 0
:
Factors to
(x+30)(x-25) = 0
:
the positive solution
x = 25 km/h is A's speed
then
25 + 5 = 30 km/h is B's speed
:
find the travel times
A: 150/25 = 6 hrs
B: 150/30 = 5 hrs
:
:
1.2) Calculate at what time they will reach C.
9:00 + 6 = 3 PM; A will reach C
and
10:00 + 5 = 3 PM; B will reach C also