## Thursday, July 9, 2009

### Wedding Planner

You are a wedding planner and you are scheduled to arrive at the wedding in another town at 6pm. From your past experience, you know that if you travel at 80 miles per hour, you would reach the town at 5pm, one hour earlier. If you travel at speed of 40 miles per hour, you would arrive at 7pm, an hour late. How fast should you travel to arrive precisely at 6pm and how far is this town?

Anonymous said...

The town is 160 miles away, and you should travel at 53.333333333 miles/hour to get there at 6 pm.
distance (X)= speed(80) x time (Y) = 40 x (Y + 2)
So X is 160 miles, Y is 2 hours. Alina

Maria said...

Right on, Alina!
I will repeat it step-by-step here for those who like me need every detail to get it:
Alina marked the distance to the town as X and the time you traveled when you drove with the speed 80mph, as Y.
Then, for the trip with the speed 80mph we have:
distance = speed x time
X = 80 x Y

For the trip with speed of 40mph:
X = 40 x (Y + 2)
as it you arrived at 7pm instead of 5pm

from this, we have:
80 x Y = 40 x (Y+2)
40 x Y = 80
Y = 2 (hours)
X = 80 x Y = 160 (miles)

so, when you traveled with a speed of 80mph and arrived at 5pm, it took you Y=2 hours.
If you want to leave at the same time and get there at 6pm instead of 5pm, you will be traveling 3 hours.

160 miles / 3 hours = 53.33mph