You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression
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What is an extraneous solution?</h3>
An extraneous solution is a solution that in obtained after completely solving an equation but it does not work in the original given equation.
You should must check for an extraneous solution when the variable appears both inside and outside the absolute value expression (Option D).
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<span>Let x = the miles Jeanie ran
y = the miles Jeanie biked
T = 2 hours total time for the duathlon
v1 = 8.5 mph Jeanie's running speed and
v2 = 16 mph Jeanie's biking speed
But T = Jean's time she ran t1 + time she biked t2 I. e t1 + t2 = 2
So we have average speed v2 when she biked = distance (y) / time (t2)
Distance y = v2 * t2 = 16 * t2 and distance when she ran x = 8.5 * t1
Since she covered 27 miles while running and biking we have
x + y = 27
8.5t1 + 16t2 =27 ------(1)
t1 + t2 = 2 --------------(2)
The simultaneous equation gives us
t1 = 2/3 and t2 which is time she biked = 4/3
So 4/3 = 1 1/3. Which is 1 hour 20 minutes</span>
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