Answer:
The total distance is 41/9 = 4 5/9 miles
Step-by-step explanation:
Total time is 2 1/2 hours.
First hour, he walks 1 2/3 = 5/3 miles.
Second hour, he walks 1 3/4 = 7/4 miles.
The last half hour he walks 1/4 of total distance. If we call total distance x.
[tex]\frac{5}{3} + \frac{7}{4} +\frac{x}{4} = x[/tex]
Now, we can eliminate the denominator, multiplying by four and by three.
[tex]5*4 + 7*3 + 3*x = 4*3*x\\20 + 21 + 3x = 12 x\\41 +3x = 12x \\41 = 12x - 3x\\41 = 9x\\x = 41/9\\x = 4 \frac{5}{9}[/tex]
Total distance is 4 5/9 miles
