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Nata [24]
2 years ago
12

Ali hops on his 3 wheeler and heads off at 12 mph. Two hours later, Fatimah chases after him on a moped at 18 mph. How far will

Ali get before Fatimah overtakes him? Write the system equations.
Mathematics
1 answer:
mash [69]2 years ago
3 0

Answer: 72 miles.

Step-by-step explanation:

We know the relationship:

Distance = speed*time.

Then we can write the equation for distance as a function of time for Ali as:

A(t) = 12mph*t

where t is time in hours.

Fatimah's equation will be:

F(t) = 18mph*(t - 2h)

where the -2h appears because she starts two hours after Ali.

Fatimah will overtake Ali when F(t) = A(t) (their positions are the same)

Then we need to solve:

12mph*t = 18mph*(t - 2h)

12mph*t = 18mph*t - 18mph*2h

12mph*t = 18mph*t - 36 mi

36 mi = (18mph - 12mph)*t

36mi = 6mph*t

36mi/6mph = t

6h = t

So Ali travels for 6 hours before he gets overtaken, then the total distance that Ali travels is:

A(6h) = 12mph*6h = 72 mi

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​

 

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The second equation is solved for xxx, so we can substitute the expression -y+3−y+3minus, y, plus, 3 in for xxx in the first equation:

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The solution to the system of equations is x=-3x=−3x, equals, minus, 3, y=6y=6y, equals, 6.

We can check our work by plugging these numbers back into the original equations. Let's try 3x+y = -33x+y=−33, x, plus, y, equals, minus, 3.

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Example 2

We're asked to solve this system of equations:

\begin{aligned} 7x+10y &= 36\\\\ -2x+y&=9 \end{aligned}

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In order to use the substitution method, we'll need to solve for either xxx or yyy in one of the equations. Let's solve for yyy in the second equation:

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Now we can substitute the expression 2x+92x+92, x, plus, 9 in for yyy in the first equation of our system:

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