A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles
<h3>How can the length of the third ride be calculated?</h3>
The base fare = $2.00
Let <em>x </em>represent the per-mile rate, and let <em>y </em>represent the per-minute rate, we have;
The cost of Ryan's first taxi ride = $8.50
Distance traveled in the first ride = 3.0 miles
Time taken during the first ride = 7 minutes
Therefore;
2 + 3•x + 7•y = 8.5
Which gives;
3•x + 7•y = 8.5 - 2 = 6.5
Distance traveled in the second ride = 7.0 miles
Duration of the second ride = 14 minutes
The second ride cost = $16.00
Therefore;
2 + 7•x + 14•y = 16
Which gives;
7•x + 14•y = 16 - 2 = 14
Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;
(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1
x = 1
- The per-mile rate, <em>x </em>= $1
3•x + 7•y = 6.5
7•y = 6.5 - 3•x
7•y = 6.5 - 3×1 = 3.5
y = 3.5/7 = 1/2 = 0.5
- The per-minute rate, <em>y </em>= $0.5
Duration of the third taxi ride = 10 minutes
Cost of the third ride = $13.50
Therefore;
2 + 1×a + 10×y = $13.50
Where <em>a </em>is the distance traveled during the third ride, we have;
2 + 1×a + 10×0.5 = $13.50
2 + a + 5 = 13.5
a = 13.5 - 2 - 7 = 4.5
- The third ride was, <em>a </em>= 4.5 miles
Learn more about simultaneous linear equations here:
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