SOLUTION: one car travels 300 miles in the same amount of time it takes a second car traveling 5 miles per hour slower than the first to go 275 miles. what are the speeds of the two cars

Question 832098: one car travels 300 miles in the same amount of time it takes a second car traveling 5 miles per hour slower than the first to go 275 miles. what are the speeds of the two cars
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
What if you are not given specific number values?
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One car travels d miles in the same amount of time it takes a second car traveling k miles per hour slower than the first to go e miles. what are the speeds of the two cars?

What are you given?
Fast Car
d = 300 miles
r = speed for fast car
Slow Car
e = 275 miles
k = how much slower is the slower car, a "miles per hour less" number
r -k = speed for slow car
Both Cars
t, amount of time is equal for both cars.
UNKNOWNS: r and t.
KNOWNS: d, e, k.

WHICH CAR__________speed____________time___________distance
FAST_______________r________________t_______________d
SLOW______________r-k_______________t______________e

The question is to find r, but the question does not ask for t. Not really any trouble about t, because it will be equal for both cars.

We still make some use of t.
for rate, time, distance, so

Fast Car equation,
Slow Car equation,
-
The two expressions for t are equal.

And because reciprocals will also be equal,

Multiply both members by the common denominator of ;

Multiply both members by negative 1,

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THAT is a formula for r, the FAST car.
Return to the list of variables, substitute their values, and compute r.

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Within sensible reason, you can use this solution and formulas for any general situation fitting the form for the description, no matter (almost) the values for fast or slow vehicles or what is moving in that equal amount of time. You could choose different variables if you want.
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
one car travels 300 miles in the same amount of time it takes a second car traveling 5 miles per hour slower than the first to go 275 miles. what are the speeds of the two cars

Slower car's speed: mph
Faster car's speed: mph
You can do the check!!
If you need a complete and detailed solution, let me know!!
Send comments, �thank-yous,� and inquiries to �D� at MathMadEzy@aol.com.
Further help is available, online or in-person, for a fee, obviously.

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