Question

Each morning, John jogs at 6 miles per hour and rides a bike at 12 miles per hour. His goal is to jog and ride his bike a total of at least 9 miles in less than 1 hour. If John jogs j miles and rides his bike b miles, which of the following systems of inequalities represents John’s goal?

• A. $\frac{j}{6}+\frac{b}{12}<1;j+b\ge 9$
• B. $\frac{j}{6}+\frac{b}{12}\ge 1;j+b<9$
• C. $6j+12b\ge 9;j+b<1$
• D. $6j+12b<1;j+b\ge 1$

Answer 1

The correct option is A $\frac{j}{6}+\frac{b}{12}<1;j+b\ge 9$

Given that John jogs for j miles and rides his bike for b miles. Also, jogging speed = 6 mph and riding speed = 12 mph
Time spent jogging = $\frac{j}{6}$ hours
Time spent riding = $\frac{b}{12}$ hours
Total time = $\frac{j}{6}+\frac{b}{12}$
Since, total time taken must be less than 1 hour, $\frac{j}{6}+\frac{b}{12}<1$
Total distance covered = (j + b) miles
Since total distance covered must be at least 9 miles, $j+b\ge 9$
Correct choice is A.