Question

Amy initially 5.0 mi west of the United Center's Michael Jordan statue is running with a constant velocity of 5.0 mi/h due east. Alejandro is initially 4.0 mi east of the statue and is running with a constant velocity of 7.0 mi/h due west. How far are the runners from the statue when they meet?

Answer 1

The statue is 1.67 miles west of both the runners

Step-by-step explanation:

Wherever Amy and Alejandro meet they will have covered a total distance of 5+4 = 9 mi

They will also have run the same amount of time if they started at the same moment = t

Speed of Amy = 5 mi/h

Speed of Alejandro = 7 mi/h

Distance = Speed × Time

Distance travelled by Amy = 5t

Distance travelled by Alejandro = 7t

Total distance run by Amy and Alejandro is

5t+7t = 9

`\\\Rightarrow 12t=9\\\Rightarrow t=(12)/(9)\\\Rightarrow t=(4)/(3)\ hours`

Distance travelled by Amy

`5* t=5* (4)/(3)=(20)/(3)\\ =6.67\ miles`

The distance of Amy from the statue would be

6.67 - 5 = 1.67 miles

So, the statue is 1.67 miles west of both the runners