<PRE><B>Question 155228</B>
1. Charles and Melanie are 100 km apart and are driving at constant speeds.
 If they drive toward each other, they will meet in 1 hr. If they drive in
 the same direction, he will overtake her in 5 hr. Find their speeds.
;
Let x = C&#39;s speed
Let y = M&#39;s speed
:
When they are driving towards each other, their speeds are additive:
Write a distance equation, Dist = time * speed
1(x+y) = 100
x + y = 100
or
y = (100-x)
:
Write another distance equation, when they go the same direction.
C has to travel has to travel 100 further than M in the same time (5 hrs)

5x - 100 = 5y
Replace y with (100-x)
5x - 100 = 5(100-x)
:
5x - 100 = 500 - 5x
:
5x + 5x = 500 + 100
:
10x = 600
:
x = 60 km/hr is C&#39;s speed
Find M&#39;s speed
y = 100 - 60
y = 40 km/hr is M&#39;s speed
:
Check solutions using the distance
5*60 = 300 km
5*40 = 200 km
--------------
diff = 100 km
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:
2. Wayne invested part of his money at 8% and the rest at 6%. The income from 
both investments totaled $2,000. If he interchanged his investments, his
 income would increase by $340. How much did he have in each investment?
:
Originally: x = amt invested at 8% and y = amt invested at 6%
:
.08x + .06y = 2000; original income equation
.06x + .08y = 2340; switched income equation
:
Multiply the 1st equation by 8, and the 2nd equation by 6; results
.64x +.48y = 16000
.36x + 48y = 14040
----------------------subtraction eliminates y, find x
.28x + 0y = 1960
:
x = {{{1960/28}}}
x = $7,000 originally invested at 8%
:
Find y:
.08(7000) + .06y = 2000
560 + .06y = 2000
.06y = 2000 - 560
.06y = 1440
y = {{{1440/.06}}}
y = $24,000
:
:
Check solution by switching the investments
.08(24000) + .06(7000) =
1920 + 420 = 2340; confirms our solutions
;
:
Do you have any questions about either of these? did you understand what we did?

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