Question 837774: At 6 A.M. a snowplow, traveling at a constant speed, begins to clear a highway leading out of town. At 8 A.M. an automobile begins traveling the highway at a speed of 35 mi/hr and reaches the plow 20 minutes later. Find the speed of the snowplow.
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website! At 6 A.M. a snowplow, traveling at a constant speed, begins to clear a highway leading out of town. At 8 A.M. an automobile begins traveling the highway at a speed of 35 mi/hr and reaches the plow 20 minutes later. Find the speed of the snowplow.
Make this chart:
distance rate time
----------------------------------------
snowplow
car
Let x = the snowplow's rate.
The car begins at 8AM and reaches the snowplow at 8:20AM.
So the car's travel time is 20 minutes or 20/60 or 1/3 hour.
The snowplow begins at 6AM and plows till 8:20AM when the car catches up.
So the snowplow's time is 2 hours 20 minutes or 2 1/3 hours, or 7/3 hours.
The car's rate is 35 mph,
So fill those four in:
distance rate time
----------------------------------------
snowplow x 7/3
car 35 1/3
Now fill in the distances using distance=(rate)(time)
The snowplow's distance = (rate)(time) = x(7/3) = (7/3)x
The car's distance = (rate)(time) = 35(1/3) = 35/3
Fill those in
distance rate time
----------------------------------------
snowplow (7/3)x x 7/3
car 35/3 35 1/3
They go the same distance, so we set the two
distances equal to each other:
(7/3)x = 35/3
Multiply both sides by 3
7x = 35
Divide both sides by 7
x = 5
The snowplow is going 5 mph.
Edwin
|
|
|
