I need help please!!

Question

1. Step 1. Read the problem. Make sure all the words and ideas are understood.
2. Step 2. Identify what we are looking for.
3. Step 3. Name what we are looking for. Choose a variable to represent that quantity.
4. Step 4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.
5. Step 5. Solve the equation using good algebra techniques.
6. Step 6. Check the answer in the problem and make sure it makes sense.
7. Step 7. Answer the question with a complete sentence.

Two cars start from start from towns 630 mi apart and travel toward each other. They meet after 6 hr. Find the speed of each car if one travels 25 mph faster than the other.

Show all steps!

Answer 1

Faster car went 65 mph, Slower car went 40 mph

You're looking for the speed of each car, which appears to be a constant

Let F = the speed of the faster car

Let S = the speed of the slower car

then F= 25+ S

The faster car goes a distance of D

the slower car goes a distance of 630-D

distance = rate of speed x time

both traveled the same time of 6 hours

d=rt or

t= d/r, time = distance/speed

for the Faster car, 6= D/F or 6F=D

for the Slower car 6= (630-D)/S = (630-D)/(F-25)

6=(630-D)(F-25)

now substitute 6F for D

6=(630-6F)(F-25)

expand and solve for F

6=-6F^2 + 780F - 15750

F^2 - 780F + 15756 = 0

discriminate = b^2 -4ac, b=-780, a = 1, c= 15,756

the discriminate is positive: 780^2 - 4(1)(15756) = 541,476

there are two solutions, altho one may be negative

either factor, complete the square or use the quadratic formula to solve for F

the following is completing the square on each side so you can take the square root

F^2 -780F + (780/2)^2 = -15,756 + (780/2)^2

(F-390)^2 = 152,100-15,756 = 136,344

F-390 = + or - sqr136,344

F = 390 + or - 369.25 = 759.25 or 31.75 mph

then S = 734.25 or 6.75

the 700+ speeds make no sense as they would have finished the distances in less than an hour, never 6 hours.

so F= 31.75 mph and S= 6.75 mph

F is 25 mph faster than S

6 x 6.75 = 40.5 miles

6 x 31.75 = 190.5 miles

added together gives 231 miles

They don't add up to 630 miles

There's a mistake somewhere, so you recheck each step.

Had each gone the same speed, the speed would have been 630/6 = 105 mph

divide by 2 to get 52.5.

If one is 25 more than the other, odds are the speeds were 65 mph and 40 mph

by adding 25/2 to 52.5 and subtracting 25/2 to 52.5, to keep the two speeds 25 mph difference.

6 x 40 = 240

6x65= 390

240+390 = 630

the two speeds of the cars were 40 mph and 65 mph

the algebraic method was so tedius mistakes arose

but looking at what is realistic led to the actual solution.