You are driving home from school steadily at 65 mph for 130 miles. It then begins to rain and you slow to 55 mph. You arrive home after driving 3 hours and 20 minutes. (a) How far is your hometown from school? (b) What was your average speed? --- I know that you need distance traveled in order to find part b ( average speed) but how do you find distance traveled?
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You need to find the TIME for each segment.
In the first section 65 mph for 130 miles
we have v = s/t or t = s/v = 130 / 65 = 2 hrs
Therefore he went at 55 mph for 1hr and 20 minutes ( = 4/3 hrs)
In this time he moved 55 * 4/3 = 73 miles
so the total distance travelled was 130 + 73 = 203 miles
and the total time was given as 3hr 20 = 10/3 hrs
so average speed is distance / time = 203 * 3/10 = 60.9 mph
In the first section 65 mph for 130 miles
we have v = s/t or t = s/v = 130 / 65 = 2 hrs
Therefore he went at 55 mph for 1hr and 20 minutes ( = 4/3 hrs)
In this time he moved 55 * 4/3 = 73 miles
so the total distance travelled was 130 + 73 = 203 miles
and the total time was given as 3hr 20 = 10/3 hrs
so average speed is distance / time = 203 * 3/10 = 60.9 mph
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Answers -->
(a) Distance from home to school is 155.8 miles
(b) Average speed is 46.7 miles per hour.
This is pretty straightforward. But it looks mean. It's not.
r1 = 65 miles per hour
d1 = 130 miles
So right away, you have at least 130 miles to school. Since Distance = Rate * Time, you can calculate how long it took you to drive those 130 miles, solving for time
D = R / T
T * D = R
T = R / D
T1 = (65 mi/hr) / (130 mi)
T1 = 0.5 hours (30 minutes; units of miles canceled)
You're given the total time
TT = 3 hr, 20 min
Put that in terms of minutes
(3 hr) * (60 min / 1 hr) = 180 minutes + 20 minutes = 200 minutes
You know you were driving the first leg only took 30 minutes, so the remaining leg took
T2 = (200 min) - (30 min)
T2 = 170 min
Now you have time and speed for the second leg, you can solve for distance (put hours in terms of minutes for the equation)
D = (55 mi/hr) * ( hr / 60 min) * ( 170 min) <--- ( 1 hr / 60 min) converted to minutes
Distance from home to school = 155.8 miles
Now on to the second part.
You know total time (200 minutes) and you know total distance (155.8 miles), just solve for total average speed, using a conversion back to hours (60 min/hr)
R = (155.8 mi) / (200 min)
R = (0.779 miles/min) * (60 min/hr)
R = 46.7 miles per hour.
And your'e done!
(a) Distance from home to school is 155.8 miles
(b) Average speed is 46.7 miles per hour.
This is pretty straightforward. But it looks mean. It's not.
r1 = 65 miles per hour
d1 = 130 miles
So right away, you have at least 130 miles to school. Since Distance = Rate * Time, you can calculate how long it took you to drive those 130 miles, solving for time
D = R / T
T * D = R
T = R / D
T1 = (65 mi/hr) / (130 mi)
T1 = 0.5 hours (30 minutes; units of miles canceled)
You're given the total time
TT = 3 hr, 20 min
Put that in terms of minutes
(3 hr) * (60 min / 1 hr) = 180 minutes + 20 minutes = 200 minutes
You know you were driving the first leg only took 30 minutes, so the remaining leg took
T2 = (200 min) - (30 min)
T2 = 170 min
Now you have time and speed for the second leg, you can solve for distance (put hours in terms of minutes for the equation)
D = (55 mi/hr) * ( hr / 60 min) * ( 170 min) <--- ( 1 hr / 60 min) converted to minutes
Distance from home to school = 155.8 miles
Now on to the second part.
You know total time (200 minutes) and you know total distance (155.8 miles), just solve for total average speed, using a conversion back to hours (60 min/hr)
R = (155.8 mi) / (200 min)
R = (0.779 miles/min) * (60 min/hr)
R = 46.7 miles per hour.
And your'e done!
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distance is 130 + 55*80/60=203.3333miles
speed =203.333333/(200/60) =61 miles/hour
speed =203.333333/(200/60) =61 miles/hour
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t = S1/V1 = 130/65 = 2 hrs. So S = S1 + V2(T - t) = 130 + 55*(3.3 - 2) = 201.5 miles to the house. a)
Vavg = 201.5/3.2 = 63.0 mph b)
Vavg = 201.5/3.2 = 63.0 mph b)