SOLUTION: The first two sections of a bicycle race are x and y meters long. Annie cycles the first part of the race at 6m/s and the second part at 12m/s. Barry cycles the same sections at 10

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Question 557423: The first two sections of a bicycle race are x and y meters long. Annie cycles the first part of the race at 6m/s and the second part at 12m/s. Barry cycles the same sections at 10m/s and 6m/s. It takes Annie half a minute to cycle these two sections, whereas it takes Barry 46 seconds to cover the same distance.
How long are these two sections of the race?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The first two sections of a bicycle race are x and y meters long.
Annie cycles the first part of the race at 6m/s and the second part at 12m/s
Barry cycles the same sections at 10m/s and 6m/s. It takes Annie half a minute to cycle these two sections, whereas it takes Barry 46 seconds to cover the same distance.
How long are these two sections of the race?
:
Write a time equation for each; time = dist/speed. simplify each equation
:
First cyclist:
x%2F6 + y%2F12 = 30
Multiply by 12, to clear the denominators, results
2x + y = 360
:
2nd cyclist: x%2F10 + y%2F6 = 46
multiply by 30
3x + 5y = 1380
Multiply the 1st equation by 5, subtract the above equation
10x + 5y = 1800
3x + 5y = 1380
----------------subtraction eliminates y, find x
7x = 420
x = 420/7
x = 60 meters is the 1st part
and
y = -2x + 360
y = -2(60) + 360
y = 240 meters is the 2nd part
:
:
Check this; find the time of the 1st cyclist
60/6 + 240/12
10 + 20 = 30 sec
and the 2nd cyclist time
60/10 + 240/6 =
6 + 40 = 46 sec