Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart?
Hint: We do know that one car is 180 miles ahead of the other, so the slow car's distance can be represented by " d " and the distance of the fast car, which would be ahead, can be represented by "d + 180." The time is the same again, and can be represented by "t." This time we have two unknowns, so we need two equations, one for the fast car, and one for the slow car. Again we are using the basic formula d = rt , and substituting the values that are relevant to our situation. The equation for the slow car is: d = 55t. You write the equation for the fast car, and solve the system by substitution. Don't forget the units in your answer.
In the same direction.
distance slow= 55*time
distance fast= 65*time
But we know the distance between= distance fast - distance slow.
180= distancefast-distanceslow
or distancefast= 180 + distanceslow.
so substutute that in the second equation.
distancefast= 65*time
180+distanceslow= 65*time
but distance slow= 55*time then
180+55*time=65*time
solve for time
180= 65*time -55*time
180= (65 -55)time
time= 18 hrs
check that.
so then the answer is 18 hours?
or do you just want me to check that?
can you just check i please.
how you get 18 hours
Yes, the answer is indeed 18 hours. To solve this problem, we need to set up two equations representing the distance traveled by each car. Let's call the time it takes for both cars to be 180 miles apart "t".
For the slow car traveling at 55 mph, the distance can be represented as d = 55t.
For the fast car traveling at 65 mph, the distance can be represented as d + 180 = 65t. Since it is traveling faster, it will be 180 miles ahead of the slow car.
To solve the system of equations, we can substitute the value of d from the first equation into the second equation:
55t + 180 = 65t.
Rearranging the equation:
180 = 65t - 55t.
Simplifying:
180 = 10t.
Dividing both sides by 10:
18 = t.
So, it will take 18 hours before the two cars are 180 miles apart.