Part A
Let's say point P is the starting point and point Q is the endpoint
x = one-way distance from P to Q, and vice versa
The goal is to find x, then compute 2x to find the round trip distance traveled.
We'll use this idea
distance = rate*time
which solves to
time = distance/rate
So when going from P to Q, the driver is going 70 mph and travels x miles
So the driver does this for distance/time = x/70 hours.
When going back, the driver slows down to 55 mph so the time taken here is x/55 hours.
The total time values add to x/70 + x/55 hours
Set this equal to the total driving time of 7 hours and solve for x
x/70 + x/55 = 7
70*55*(x/70 + x/55) = 70*55*7
70*55*(x/70) + 70*55*(x/55) = 26,950
55x + 70x = 26,950
125x = 26,950
x = (26,950)/125
x = 215.6 which is the one-way distance in miles
which then means,
2x = 2*215.6 = 431.2
Therefore, the total distance traveled is 431.2 miles
<h3>Answer: 431.2 miles</h3>
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Part B
To find the duration of each trip, we simply need to evaluate x/70 and x/55. Those are the durations when going 70 mph and 55 mph respectively. These durations are measured in hours.
x/70 = (215.6)/70 = 3.08
x/55 = (215.6)/55 = 3.92
Note how 3.08+3.92 = 7 to help verify the answers.
<h3>Answers:</h3>
- When going 70 mph, it takes about 3.08 hours
- When going 55 mph, it takes about 3.92 hours
