SOLUTION: John starts driving at a constant rate of 55 mph. Two hours later Lauren starts driving at a constant rate of 62 mph. At what time and how many miles will they meet? Create a syste

Question 1195979: John starts driving at a constant rate of 55 mph. Two hours later Lauren starts driving at a constant rate of 62 mph. At what time and how many miles will they meet? Create a system of equations and use the equal value theorem to solve
Found 3 solutions by math_tutor2020, ikleyn, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = number of hours that John is driving
x-2 = number of hours that Lauren is driving
John has a 2 hour head start, so Lauren drives 2 fewer hours.

John drives a distance of
distance = rate*time
d = r*t
d = 55*x

Lauren drives a distance of
d = r*t
d = 62*(x-2)
d = 62x-124

If we want the two drivers to meet up, then they must travel the same distance.
This assumes they started at the same point.
Equate the right hand sides and solve.
55x = 62x - 124
55x-62x = -124
-7x = -124
x = -124/(-7)
x = 17.7143 approximately

It takes about 17.7143 hours for the two drivers to meet.

Let's compute the distance traveled for each driver.
John = 55x = 55*17.7143 = 974.2865 miles
Lauren = 62(x-2) = 62*(17.7143-2) = 974.2866 miles
The results are approximate. We get a slight discrepancy due to the approximate nature of the decimal values. However, the distances are close enough. Round the decimal values however your teacher instructs.

Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
John starts driving at a constant rate of 55 mph. Two hours later Lauren starts driving at a constant rate of 62 mph.
At what time and how many miles will they meet? Create a system of equations and use the equal value theorem to solve
~~~~~~~~~~~~~

As the problem is worded, printed, posted and presented, it is ABSURDIST,

because it does not define from which point/points they started and in which direction/directions they move.

Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
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John starts driving at a constant rate of 55 mph. Two hours later Lauren starts driving at a constant rate of 62 mph. At what time and how many miles will they meet?
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You are forcing the reader to make assumptions. Best assumption is that John and Lauren started from the same departure location. Lauren left later and catches-up.

During first two hours, John traveled 110 miles. Lauren then began and her approach rate to John
was 62-55=7 miles per hour.

How much time for Lauren to cover the 110 mile difference?

About 15 hours 43 minutes
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