Barbara and her husband take a trip on a highway, a distance of 600 miles. They intend to average 60 m.p.h. and take 10 hours. However, they take 11 hours due to construction. When they encounter the construction, they reduce their speed to 40 m.p.h. and proceed at this speed until they reach their destination. How many miles from their starting point did they come to the construction?
distance at 60 mph --- x
distance at 40 mph --- 600-x
time at 60 mph = x/60
time at 40 = (600-x)/40
x/60 + (600-x/40 = 11
times 120
2x + 3(600-x) = 1320
2x+1800 - 2x = 1320
-x = -480
x=480
The encountered the construction after going 480 miles
check:
480/60 + 120/40 = 8 + 3 = 11
To find out how many miles from the starting point Barbara and her husband encountered the construction, we need to calculate the distance they traveled before encountering the construction.
First, let's calculate the distance they would have traveled if they had maintained their intended average speed of 60 m.p.h. for 10 hours:
Distance = Speed x Time
Distance = 60 m.p.h. x 10 hours
Distance = 600 miles
Since they took 11 hours instead of 10, they actually traveled at a reduced speed of 40 m.p.h. for one additional hour (11 - 10 = 1 hour).
So, in this extra hour, they traveled an additional distance of:
Distance = Speed x Time
Distance = 40 m.p.h. x 1 hour
Distance = 40 miles
Therefore, Barbara and her husband encountered the construction 40 miles from their starting point.
To find out how many miles from their starting point Barbara and her husband came to the construction, we can use the concept of average speed.
Let's call the distance from their starting point to the construction point "x" miles.
From their starting point to the construction point, they traveled at a speed of 60 m.p.h for 10 hours, covering a total distance of (60 * 10) = 600 miles.
After encountering the construction, they reduced their speed to 40 m.p.h and continued for another 1 hour (11 - 10) until they reached their destination. At this lower speed, they covered a distance of 40 miles.
So, the total distance from their starting point to their destination is 600 + 40 = 640 miles.
Since the distance from their starting point to the construction point is x miles, the remaining distance from the construction point to their destination is (640 - x) miles.
We can create an equation using the average speed concept:
Average Speed = Total Distance / Total Time
Using the equation, we can set up the following equation:
60 = (600 + 40) / 11
Now, we can solve for x:
60 = (640 - x) / 11
Multiplying both sides of the equation by 11, we get:
660 = 640 - x
Subtracting 640 from both sides, we have:
660 - 640 = -x
20 = -x
Multiplying both sides by -1, we get:
x = -20
Since distance cannot be negative, this means that the construction point is 20 miles from their starting point.
Therefore, Barbara and her husband came to the construction 20 miles from their starting point.