Question 515194: a car and a bus leave from the same spot and drive in opposite directions. the bus is travelling 11mph slower than the car. in 4.25 hours the car and bus are 174 miles apart. find the average speed of the car.
Answer by drcole(72)   (Show Source):
You can put this solution on YOUR website! Let s be the average speed of the car.
Since the bus is traveling 11 mph slower than the car, we can express the average speed of the bus as  .
The relationship between distance traveled, average speed, and time is:
Distance Traveled = (Average Speed)(Time)
Therefore, after 4.25 hours, the car has traveled
Distance Traveled by Car =  miles
while the bus has traveled
Distance Traveled by Bus =  miles (distributing the 4.25 in the last step)
We know that the car and the bus are traveling in opposite directions, and that the distance between them after 4.25 hours is 174 miles. We can express this fact algebraically as an equation:
Distance Traveled by Car + Distance Traveled by Bus = 174
Now we solve for s:
 (combine like terms)
 (add 46.75 to both sides)
 (divide both sides by 8.50)
So we get that the average speed of the car is  mph, or, to the nearest hundredth, 25.97 mph. Does this make sense? If the car is traveling at mph, after 4.25 hours it will have traveled  mph
After 4.25 hours then, the bus has traveled:
 miles
Therefore the car and the bus will be 110.375 + 63.625 = 174 miles apart after 4.25 hours, so our solution works.
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