SOLUTION: if a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip?

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Question 227740: if a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip?
Found 2 solutions by stanbon, drj:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip?
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The difference in the time is 4 hours.
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1st car DATA:
rate = 55 mph ; distance = x miles ; time = d/r = x/55 hrs
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2nd car DATA:
rate = 35 mph ; distance = x miles ; time = d/r = x/35 hrs
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Equation:
slower time - faster time = 4 hrs
x/35 - x/55 = 4
55x - 35x = 4*35*55
20x = 7700
x = 385 miles (length of the trip)
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Cheers,
Stan H.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip?

Step 1. distance = speed * time

Step 2. Let t be the time of the trip traveling on time.

Step 3. Let t-2 be the time if traveling at 55 mph.

Step 4. Let 55(t-2) be the distance traveling at 55 mph.

Step 5. Let 35(t+2) be the distance traveling at 35 mph.

Step 6. Then, 55(t-2)=35(t+2) since the distances are equal in Steps 4 and 5.

Step 7. Solving the equation in Step 6 yields the following steps

55t-110=35t%2B70

Add 110-35t to both sides of the equation

55t-110%2B110-35t=35t%2B70%2B110-35t

20t=180

Divide by 20 to both sides of the equation

20t%2F20=180%2F20

t=9

Substitute the value of t in Steps 4 or 5. We'll do both to check if distances are equal

55%289-2%29=385 miles and 35%289%2B2%29=385 miles.

Step 8. The distance is 385 miles.

I hope the above steps were helpful.

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Respectfully,
Dr J
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