Question 142209
1. Maria bicycles 5 km/h faster than Carlos . In the same time it takes Carlos to bicycle 30 km, Maria can bicycle 45 km. How fast does each bicyclist travel?
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Let s = C's speed
then
(s+5) = M's speed
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Write a time equation: Time = dist/speed
;
C's time = M's time
{{{30/s}}} = {{{45/((s+5))}}}
Cross multiply:
45s = 30(s+5)
45s = 30s + 150
45s - 30s = 150
15s = 150
s = 10 km/hr is C's speed, 15 km/hr is M's speed
:
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check solutions by confirming that the times are the same:
30/10 = 3 hr
45/15 = 3 hr
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2. hat size head circum. (to nearest 1/5 inch) head circum to nearest cm
7 3/8 23 1/5 59
-???- ?????- 58
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Find the relationship of cm to inches: {{{59/(23.2)}}} = 2.54 cm in 1 inch
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Convert 58 cm to inches: {{{58/2.54}}} = 22.83 inches or 22{{{4/5}}}inches
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Find the relationship of circumference in inches to hat size
{{{7.375/23.2}}} = .318
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Multiply 22.8 * .318 = 7.24 or 7{{{1/4}}}(hat size)
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Fill in the table as follows:
7 3/8....23 1/5...59
7 1/4....22 4/5...58
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