Answer:
33 miles
Step-by-step explanation:
Trip to airport:
distance = d1
speed = s1 = 55 mph
time = t1
Trip home:
distance = d2
speed = s2 = 45 mph
time = t2
We are told the same route was used for both trips, so
d1 = d2
The total time was 1 hr 20 min = 1 hr + 20/60 hr = 4/3 hr.
t1 + t2 = 4/3
t2 = 4/3 - t1
speed = distance/time
distance = speed * time
d1 = s1 * t1
d2 = s2 * t2
d1 = d2, so
s1 * t1 = s2 * t2
t2 = 4/3 - t1; s1 = 55; s2 = 45
55 * t1 = 45(4/3 - t1)
55t1 = 60 - 45t1
100t1 = 60
t1 = 0.6
The time to get the the airport was 0.6 hr. Now we find the distance.
d1 = s1 * t1
d1 = 55 * 0.6
d1 = 33
The distance is 33 miles.
The airport is at a distance of 33 miles from Dara's home.
Speed is directly proportional to distance and inversely proportional to time. Its equation is given as:
Speed = Distance/Time.
The other equations, formed using this equation are:
Distance = Speed*Time
Time = Distance/Speed.
In the question, we are informed that Dara drove from home to the airport to pick up her friend and then came back home on the same route. Her average speed on the way to the airport was 55 miles per hour (mph), and her average speed on the way back home was 45 mph.
We are asked to find the distance between Dara's home and the airport, if the total driving time was 1 hour 20 minutes.
We assume the distance between Dara's home and the airport to be x miles.
As she went to the airport and came back from the airport via the same route, her distance in both the cases will be x miles.
Time taken by Dara to go from home to the airport,
t1 = Distance/Speed = x/55 (Since, her average speed on the way to the airport was 55 mph).
Time taken by Dara on the way back home,
t2= Distance/Speed = x/45 (Since, her average speed on the way back home was 45 mph).
Now, total driving time can be written as,
t1 + t2,
= x/55 + x/45,
= (9x + 11x)/495,
= 20x/495,
= 4x/99.
Now, we know that this time is given as 1 hour and 20 minutes = 1 1/3 hours = 4/3 hours.
Therefore, we an write the equation:
4x/99 = 4/3,
or, x = (4*99)/(4*3) = 33.
Therefore, the airport is at a distance of 33 miles from Dara's home.
Learn more about speed, distance, and time at
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