If you need to find the distance between two bodies traveling at right angles away from each other, you must use the Pythagorean Theorem: a2 + b2 = c2 in addition to D = RT.
Examples
A car passes under a railway trestle at the
same time a train is crossing the trestle. The car is headed south at an
average speed of 40 mph. The train is traveling east at an average speed of 30
mph. After how long will the car and train be 10 miles apart?
Let t
represent the number of hours after the train and car pass each other. (Because
the rate is given in miles per hour, time must be given in hours.) The distance
traveled by the car after t hours is 40t and that of the train is 30t:
After ⅕ of an hour (or 12 minutes) the car
and train will be 10 miles apart.
Practice
1. A car and plane leave an airport at the same
time. The car travels eastward at an average speed of 45 mph. The plane travels
southward at an average speed of 200 mph. After how long will they be 164 miles
apart?
2. Two joggers begin jogging from the same
point. One jogs south at the rate of 8 mph and the other jogs east at a rate of
6 mph. When will they be five miles apart?
3. A cross-country cyclist crosses a railroad
track just after a train passed. The train is traveling southward at an average
speed of 60 mph. The cyclist is traveling westward at an average speed of 11 mph.
When will they be 244 miles apart?
4. A motor scooter and a car left a parking lot
at the same time. The motor scooter traveled north at 24 mph. The car traveled
west at 45 mph. How long did it take for the scooter and car to be 34 miles apart?
5. Two cars pass each other at 4:00 at an
overpass. One car is headed north at an average speed of 60 mph and the other
is headed east at an average speed of 50 mph. At what time will the cars be 104
miles apart? Give your solution to the nearest minute.
Solutions
1. Let t represent the number of hours each has
traveled. The plane’s distance after t hours is 200t and the car’s distance is
45t.
The car and plane will be 164 miles apart
after 0.80 hours or 48 minutes.
2. Let t represent the number of hours after the
joggers began jogging. The distance covered by the southbound jogger after t
hours is 8t, and the distance covered by the eastbound jogger is 6t.
The joggers will be five miles apart after ½ hour
or 30 minutes.
3. Let t represent the number of hours after the
cyclist crosses the track. The distance traveled by the bicycle after t hours
is 11t and the distance traveled by the train is 60t.
After four hours the cyclist and train will
be 244 miles apart.
4. Let t represent the number of hours after the
scooter and car left the parking lot. The car’s distance after t hours is 45t.
The scooter’s distance is 24t.
The car and scooter will be 34 miles apart
after 2 3 of an hour or 40 minutes.
5. Let t represent the number of hours after the
cars passed the overpass. The northbound car’s distance after t hours is 60t and
the eastbound car’s distance is 50t.
The cars will be 104 miles apart after about
1.33 hours or 1 hour 20 minutes. The time will be about 5.20.
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