Friday

March 6, 2015

March 6, 2015

Posted by **Suzy** on Sunday, November 28, 2010 at 11:57am.

During this time, a messenger on a horse travels from the rear of the battalion to the

front and immediately turns around, ending up precisely at the rear of the battalion

upon the completion of the 20-mile journey. How far has the messenger traveled?

- math -
**MathMate**, Sunday, November 28, 2010 at 2:07pmAn interesting problem!

We have to realize that the speed of the battalion is irrelevant. It is the ratio of the speed of the messenger, with respect to the battalion that matters.

Assume the battalion's speed is 1 mph, thus we look for the speed of the messenger y mph.

Time for messenger to go to the front,

t1= 20 miles / (y-1)

Time for messenger to go back to the rere,

t2 = 20 miles / (y+1)

So the messenger has advanced (t1-t2)y miles over the mission, or

y(t1-t2)=20

20y/(y-1)-20y/(y+1) = 20

y cannot be 1 (or he'll never catch up), so we can multiply both sides by (y-1)(y+1) to get:

20y(y+1)-20y(y-1) = 20(y-1)(y+1)

Simplifying

y²-2y-1=0

Solve the quadratic to get:

y=1+√2

Check:

y(20/(y+1)-20/(y-1))=20 OK.

Solve for total distance travelled

= y(t1+t2)

(approx. 48.3 miles)

**Answer this Question**

**Related Questions**

work - 1. You are a member of Special Troop Battalion, 3d BCT, 10th Mountain ...

algebra (23) - How do you set up this problem? A boater travels 16 miles per ...

math - 13. If two planes leave the same airport at 1:00 PM, how many miles apart...

please help! - I'm having trouble with this word problem. Two friends Jodi and ...

work - 1. You are a member of Special Troop Battalion, 3d BCT, 10th Mountain ...

algebra 1 - Two vans leave town at the same time going in opposite directions. ...

Algebra - 2 cyclists travel opposite on circular trail that is 5 miles long. one...

math - Currently, the Toyota Corolla is the best selling car in the world. ...

math - Currently, the Toyota Corolla is the best selling car in the world. ...

math algebra - Two trains leave the station at the same time, one heading east ...