A person takes a trip, driving with a constant speed of 99.5 km/h, except for a 24.0-min rest stop. The person's average speed is 66.4 km/h.
how far does the person travel?
T = total time
t-24/60 = driving time
d=99.5km/hr(T-24/60)
and, 66.4=d/T
so you have two equations, two unknowns: d and T
d=99.5T-99.5*24/60=66.4/T
so put that in quadratic form, and solve for T.
99.5T^2-99.5*24/60 T-66.4=0
when you get T, then solve for d
oops: watch the units
(66.4km/hr) / (t hr) = 66.4/t km/hr^2
I'd say:
total distance: 99.5(t - 24/60)
avg speed = distance/time
99.5(t - 24/60)/t = 66.4
t = 1.202
distance is thus 99.5(1.202 - 24/60) = 79.8 km
To find the distance traveled, we need to use the formula: distance = speed × time.
Let's break down the trip into two parts:
Part 1: Driving at a constant speed of 99.5 km/h.
Part 2: Rest stop of 24 minutes.
First, let's find the distance traveled during Part 1. We can use the formula mentioned earlier:
distance1 = speed1 × time1
Given that the speed during Part 1 is 99.5 km/h and the time is unknown, we can rewrite the formula as:
distance1 = 99.5 km/h × time1
Next, let's find the distance traveled during Part 2, the rest stop. Since the person isn't moving during this time, the distance traveled is 0 km.
Now, let's find the distance traveled during the entire trip. Adding the distances from Part 1 and Part 2:
total distance = distance1 + distance2
Since distance2 is 0 km, we can simplify the equation:
total distance = distance1
To find the time spent during Part 1, we need to know the duration of the rest stop, which is given as 24.0 minutes. But, we need to convert this time to hours, as the speed is in km/h.
time1 = total time - time2
The total time is the time taken for the trip, and it's given as the entire time spent during the trip, including the rest stop:
total time = time1 + time2
Substitute the given average speed and the total time into the equation:
66.4 km/h = total distance / (time1 + time2)
Now, we can rearrange the equation to find the total time:
total time = distance1 / 66.4 km/h
Finally, substitute the given values into the equation to find the total distance:
total distance = distance1 = 99.5 km/h × (total time - 24.0 min)
Now, let's calculate the distance traveled using this equation.