SOLUTION: a truck can travel 120 miles is the same time that it takes a care to travel 180 miles. if the truck's rate is 20 mph slower than the car's, find the adverage rate of each

Question 243043: a truck can travel 120 miles is the same time that it takes a care to travel 180 miles. if the truck's rate is 20 mph slower than the car's, find the adverage rate of each
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
This problem is nicely set up for you because you are told they two vehicles take equal time. And we know that D = RT, which means D/R = T.
We also are told the two distances:
The distance the truck travels in 'T' time = 120 miles
The distance the car travels in 'T' time = 180 miles
So we can pose the equation as:
120/x = 180/y
where x=truck's speed and y=car's speed.
We also are told x is 20 mph less than y, so we can express this as either x + 20 = y OR x = y - 20.
We're now setup to solve it.
Let's substitute: x = y -20
120/(y -20) = 180/y
Cross multiplying, we have:
120y = 180(y -20) = 180y - 3600
Subtracting 180y from both sides
-60y = -3600
Dividing by -60
y = 60
Given that x = y - 20, we expect
x = 40
But we have to check our work to see if this answer 'works'...
120/x = 3, which means the truck takes 3 hrs to go 120 miles
180/y = 3, which means the car takes 3 hrs to go 180 miles
That certainly meets the problems stated requirements, so we're done.
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