Buggs made the trip at 40 mph during the first Hiatus. Joan Made the same trip at 50 mph during the second hiatus. How long was the trip if it took Buggs 2 hours longer than it took Joan.
I know the Distance equals rate X Time and I tried using that meathod three times but i keep coming up with a negative time and i know that that is wrong will someone lead me on the right path???
name rate time distance
Buggs 40___t_____D
Joan- 50 (t-2)___D
so
40 t = 50(t-2)
40 t = 50 t - 100
-10t = -100
t = +10
time it took Joan = X
time it took Buggs = X+2 hrs.
distance each traveled is the same.
distance Joan = r*time = 50t
distance for Buggs = r*time = 40*(X+2)
40*(X+2) = 50X
solve for X = time for Joan.
X+2 = time for Buggs.
To solve this problem, let's first assign variables to the unknown values:
Let's say the distance of the trip is 'd'.
Buggs' speed is 40 mph.
Joan's speed is 50 mph.
And, Joan's time to complete the trip is 't' hours.
We know that Buggs took 2 hours longer than Joan for the same trip. So, Buggs' time to complete the trip is 't + 2' hours.
Using the formula distance = speed × time, we can write two equations based on the given information:
1) For Buggs:
d = 40(t + 2)
2) For Joan:
d = 50t
Now, we have a system of two equations.
To find the duration of the trip (t), we can solve these equations simultaneously using substitution or elimination method.
Let's use substitution method:
From equation 2), we have:
d = 50t
Now, substitute this value of 'd' into equation 1):
50t = 40(t + 2)
Expanding the equation:
50t = 40t + 80
Subtracting 40t from both sides:
10t = 80
Dividing both sides by 10:
t = 8
So, it took Joan 8 hours to complete the trip.
To find the distance of the trip (d), substitute this value of 't' into any of the two original equations.
Using equation 2:
d = 50t
d = 50 * 8
d = 400
Therefore, the distance of the trip is 400 miles.
To solve this problem, we can set up equations based on the information given and use algebra to find the answer.
Let's assign variables to the unknowns:
Let "t" be the time it took Joan to complete the trip.
Then, "t + 2" will be the time it took Buggs to complete the trip (as it took him 2 hours longer).
We know that the distance traveled by both of them is the same, let's denote it as "d".
Using the equation Distance = Rate × Time, we can set up the following equations:
For Buggs:
Distance = Rate × Time
d = 40 mph × (t + 2)
For Joan:
Distance = Rate × Time
d = 50 mph × t
Since both equations represent the same distance, we can set them equal to each other and solve for "t":
40 mph × (t + 2) = 50 mph × t
Now, let's solve for "t":
40t + 80 = 50t (multiplying through by distributing the 40 mph)
80 = 10t (subtracting 40t from both sides)
8 = t (dividing both sides by 10)
So, it took Joan 8 hours to complete the trip.
To find the distance, we can substitute this value of "t" into either of the earlier equations. Let's use Joan's equation since she took less time:
d = 50 mph × t
d = 50 mph × 8
d = 400 miles
Therefore, the distance of the trip is 400 miles.