Answer:
- 7.596 hours
- 57.596 mph
Step-by-step explanation:
a) The distance is given as ...
d = t^2 +50t
We want to find the value of t for which this distance is 437.5 miles. That means we want to solve the equation ...
437.7 = t^2 +50t
We can complete the square by adding the square of half the t coefficient, (50/2)^2 = 625
437.5 +625 = t^2 +50t +625
1062.5 = (t +25)^2
√1062.5 -25 = t ≈ 7.596 . . . . hours
It will take the truck about 7.596 hours to reach its destination.
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b) Average speed is total distance divided by total time. Here, we can find the average speed as ...
d/t = (t^2 +50t)/t = t +50
That is, the average speed over the 437.5-mile trip is ...
7.596 +50 = 57.596 . . . . miles per hour
The car must maintain a constant speed of 57.596 mph to reach the destination at the same time.
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When solving equations using a graphing calculator, I like to put them into a form such that the solution is the x-intercept. Here, that means the equation we're solving is ...
x^2 +50x -437.5 = 0 . . . . x is hours to destination
