a truck can travel 120 miles is the same time that it takes

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

Solution

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.