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earnstyle [38]
3 years ago
10

When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance

driven divided by the total time spent driving. A trucker drove 3 hours on a freeway at 60 miles per hour and then drove 20 miles in the city. The trucker’s average speed was 57.14 miles per hour.
a. Write an equation that models the situation.
b. How long was the trucker driving in the city to the nearest hundredth of an hour?
Mathematics
1 answer:
bekas [8.4K]3 years ago
3 0

a) v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}

The average speed is equal to the ratio between the total distance (d_{tot} and the total time taken (t_{tot}):

v=\frac{d_{tot}}{t_{tot}}

the distance travelled by the trucker in the first 3 hour can be written as the time multiplied by the velocity:

d_1 = (3 h)(60 mph)=180 mi

So the total distance is

d_{tot}=d_1 +d_2 = 180 mi+20 mi=200 mi

The total time is equal to the first 3 hours + the time taken to cover the following 20 miles in the city:

t_{tot}=3 h +t_2

So, the equation can be rewritten as:

v=\frac{d_{tot}}{t_{tot}}=\frac{(3 h)(60 mph)+20 mi}{3 h +t_2}


b) 0.50 h (half a hour)

Since we know the value of the average speed, v=57.14 mph, we can substitute it into the previous equation to find the value of t_2, the time the trucker drove in the city:

v=\frac{200 mi}{3h +t_2}\\3h+t_2 = \frac{200 mi}{v}\\t_2 = \frac{200 mi}{v}-3h=\frac{200 mi}{57.14 mph}-3 h=0.50 h


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