Question

After driving to a river front parking lot, Bob plans to run south along the river, turn around and return to the parking lot, running north along the same path. After running $3.25$ miles south, he decides to run for only $50$ minutes more. If Bob runs at a constant rate of $8$ minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in $50$ minutes?

Answer 1

Let the distance he walks till turning back be ${}^{\prime }{d}^{\prime }$,

Hence, total distance while returning back $=d+3.25$ miles,

Given,

time per unit mile $=8minutes$,

Total distance he walks after already completing 3.25miles $=2d+3.25miles$,

Hence, total time for this distance $=(2d+3.25)\ast 8$ $=16d+26minutes$,

Given, time to reach car after already completing 3.25 miles southwards is 50 minutes,

Hence,

$16d+26=50$;

$16d=24$;

$d=\frac{24}{16}=1.5miles$;

Hence, the required answer is 1.5 miles.