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?

• A. $1.5$
• B. $2.25$
• C. $3.0$
• D. $3.25$
• E. $4.75$

Answer 1

The correct option is A $1.5$

Step I

Since speed of Bob is $8$min/mile

$\therefore$ In 50 min he can cover $\frac{50}{8}=6.25$ miles

Step II

He ran $3.25$ miles south already & has $50$ min more, which he covers $6.25$ miles.

$\therefore$ Total dist $9.5$ miles

Step III

Since he has to go back & forth $\therefore$ $9.5/2=4.75$

He has to run $4.75$ miles south & $4.75$ miles north.

Step IV

He already traveled $3.25$ miles south & he has to travel $1.5$ miles south farther.