Question

Anna is driving from Champaign to Indianapolis on I-74. She passes the Prospect Ave. exit at noon and maintains a constant speed of 75 mph for the entire trip. Chuck is driving in the opposite direction. He passes the Brownsburg, IN exit at 12:30pm and maintains a constant speed of 65 mph all the way to Champaign. Assume that the Brownsburg and Prospect exits are 105 miles apart, and that the road is straight. How far from the Prospect Ave. exit do Anna and Chuck pass each other? x =

Answer 1

Anna and Chuck pass each other at 73.66 miles from Prospect Ave. exit.

Step-by-step explanation:

In the picture you can see that Chuck passes Brownsburg exit half hour later than Anna when she passes Prospect Ave exit. So the time when Anna and Chuck pass each other is:

`t_(C)=t_(A)-0.5 h`

Anna pass Chuck at X distance.

Chuck pass Anna at (105 miles - X) distance.

`X=V_(A)t=V_(A)t_(A)`

`105-X=V_(C)t_(C)=V_(C)(t_(A)-0.5h)`

`t_(A)=(X)/(V_(A))=(105miles-X+0.5hV_(C))/(V_(C))`

After clear X:

`X=(105miles+0.5h*V_(C))/(1+(V_(C))/(V_(A)) )`

`X=(105miles+0.5h*65mph)/(1+(65mph)/(75mph) )`

X=73.66 miles