Question 120599
 The ratio of Alex's cycling speed to Bart's cycling speed is 6:5. Bart leaves school at 3:00 pm and Alex leaves at 3:10 pm. By 3:30, Alex is only 2 km behind Bart. How fast is each boy going?
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What we know here:
At 3:30:
B's traveling time = 30 min or {{{1/2}}} hr
A's traveling time = 20 min or {{{1/3}}} hr
:
If A's speed = x
Then B's speed = {{{5/6}}}x
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Write a distance equation: Distance = time * speed
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B's dist - A's dist = 2 km
{{{(1/2)(5/6)}}}x - {{{1/3}}}x = 2
:
{{{5/12}}}x - {{{1/3}}}x = 2
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Multiply equation by 12 to get rid of the denominators
12*{{{5/12}}}x - 12*{{{1/3}}}x = 12(2)
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Cancel out the denominators and you have:
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5x - 4x = 24
x = 24 km/hr is A's speed
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{{{5/6}}}24 = 20 km/h is B's speed
:
:
Check their distances from the start at 3:30:
B travels {{{1/2}}}*20 = 10 km
A travels {{{1/3}}}*24 = 8 km; 2km difference as given