Bugs made the trip at 40 miles per hour during the first hiatus.joan made the same trip at 50 miles per hour during the second hiatus how long was the trip if it took buggs 2 hours longer than it took joan
not clear just what is happening. A hiatus is a rest period. I don't expect much traveling is done during the stops. Anyway, I'd say that if the distance traveled is x, then since time = distance/speed,
x/40 = 2 + x/50
Now just solve for x.
x=400
A good equation solving website is Math Papa. It's what I use, I know it sounds stupid but it works wonders.
Let's assume that the length of the trip is "x" miles.
We know that Bugs traveled at a speed of 40 miles per hour and took 2 hours longer than Joan. Therefore, Bugs traveled for x miles in (t + 2) hours.
Similarly, Joan traveled at a speed of 50 miles per hour for the same distance x. Therefore, Joan traveled for x miles in t hours.
We can use the formula speed = distance / time to form two equations:
For Bugs:
40 = x / (t + 2)
For Joan:
50 = x / t
To solve these equations, we can cross-multiply:
40(t + 2) = x ----> Equation 1
50t = x ----> Equation 2
Now, set the equations equal to each other:
40(t + 2) = 50t
Simplify:
40t + 80 = 50t
Rearrange the equation:
10t = 80
Solve for t:
t = 80 / 10
t = 8
Now, substitute the value of t back into either Equation 1 or Equation 2 to find the value of x:
x = 50t
x = 50 * 8
x = 400
Therefore, the length of the trip is 400 miles.
To find the length of the trip, we need to use the formula:
Distance = Speed * Time
Let's assume that the time it took Joan to complete the trip is "t" hours.
According to the question, Bugs took 2 hours longer than Joan. Therefore, the time it took Bugs to complete the trip is "t + 2" hours.
Now, let's calculate the distances traveled by Bugs and Joan:
Distance Bugs = Speed Bugs * Time Bugs = 40 * (t + 2) = 40t + 80
Distance Joan = Speed Joan * Time Joan = 50 * t = 50t
Since the distances traveled by Bugs and Joan are the same, we can equate the equations:
Distance Bugs = Distance Joan
40t + 80 = 50t
Now, let's solve for t:
40t + 80 = 50t
80 = 10t
t = 8
Therefore, it took Joan 8 hours to complete the trip. Since Bugs took 2 hours longer, his total time is 8 + 2 = 10 hours.
To find the length of the trip, we can substitute the value of t into either of the distance equations:
Distance Bugs = 40t + 80 = 40 * 8 + 80 = 320 + 80 = 400 miles
Therefore, the length of the trip is 400 miles.