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.
I think the hint is confusing. The problem is pretty straightforward to solve, but the hint suggests it's a difficult problem.
What you do is write the positions of the cars as:
d1 = 55 mph * t
and
d2 = 65 mph * t
respecrively. hen you calculate the distance fromone car to the next. It is
d2 - d1 = 65 mph * t - 55 mph * t =
10 mph * t = 10 miles *(t/hour)
If you equate this to 180 miles and solve for t, you find t = 18 hours.
Next time, don't read the hint. Hints are only useful for complicated problems where you would get stuck if you don't go about solving it in some particular way. There is little risk of that in High School.
To solve the problem, you need to calculate how much time it will take for the two cars to be 180 miles apart.
First, let's define the distance of the slow car as "d" and the distance of the fast car as "d + 180" since it is ahead.
Using the formula distance = rate * time (d = rt), we can write the equation for the slow car as: d = 55t, where t represents the time in hours.
For the fast car, the equation would be: d + 180 = 65t.
Now, we have two equations and two unknowns. We can solve the system of equations to find the value of "t" which represents the time it will take for the two cars to be 180 miles apart.
To do this, we can substitute the value of "d" from the first equation into the second equation.
Substituting d = 55t into d + 180 = 65t, we get: 55t + 180 = 65t.
By rearranging the equation, we can isolate "t" on one side. Subtracting 55t from both sides gives: 180 = 10t.
To solve for "t", we divide both sides by 10: t = 18.
Therefore, it will take 18 hours for the two cars to be 180 miles apart.
Please note that the hint provided in the problem unnecessarily complicates the solution. It is a much simpler problem and can be solved without the need for the hint.