Flying into the wind, a plane takes 8 h to travel 5432 km from Paris to Montreal. The same plane flying with the wind from Montreal to Paris takes only 7 h. Find the speed of the plane and the speed of the wind.
Can you plz answer this sir I really would appriciete it. Plz can you answer this because i have a exam tommorow and i do not want to fail so plz and thnx for all the help.
vp is plane velocity
vw is wind velocity
5432=(vp+vw)7
5432=(vp-vw)8
or
vp+vw= 5432/7
vp-vw=5432/8
add the equations...
2vp=5432(1/7+1/8) and solve for vp
then put that into either equation, and solve for vw
is the answer 727.5
thnx
You posted the same type of question
above in
http://www.jiskha.com/display.cgi?id=1232677828
Only the numbers differ.
Sure, I'd be happy to help you with this question! Let's break it down step by step.
Step 1: Assign variables
- Let's suppose the speed of the plane is represented by "p" (in km/h).
- Let's suppose the speed of the wind is represented by "w" (in km/h).
Step 2: Establish the formulas
- When flying against the wind, the effective speed of the plane will be reduced by the speed of the wind. Therefore, the formula for the time it takes to travel from Paris to Montreal is:
Time = Distance / (Speed of the plane - Speed of the wind)
In this case, the distance is 5432 km and the time is 8 hours. So we have: 8 = 5432 / (p - w).
- When flying with the wind, the effective speed of the plane will be increased by the speed of the wind. Therefore, the formula for the time it takes to travel from Montreal to Paris is:
Time = Distance / (Speed of the plane + Speed of the wind)
In this case, the distance is still 5432 km, but the time is 7 hours. So we have: 7 = 5432 / (p + w).
Step 3: Solve the equations
- We now have a system of equations with two unknowns (p and w). We can solve this system of equations to find the values of p and w.
- Let's solve this system by elimination method.
- Multiplying the first equation by (p + w) and the second equation by (p - w), we get:
8(p + w) = 7(p - w)
8p + 8w = 7p - 7w
- Now, let's simplify and bring the similar terms together:
8p - 7p = 7w + 8w
p = 15w
- We have found the relationship between p and w: p = 15w.
Step 4: Substitute the value in any equation
- We can now substitute this relationship back into one of the original equations to find one of the variables.
- Let's substitute the value of p into the first equation:
8 = 5432 / (15w - w)
8 = 5432 / 14w
- Cross-multiplying, we get:
8 * 14w = 5432
112w = 5432
w = 5432 / 112
w = 48.57 km/h (approximately)
Step 5: Find the other variable
- Now that we have found the value of w, we can substitute it back into the relationship we found between p and w to find p:
p = 15w
p = 15 * 48.57
p = 728.57 km/h (approximately)
So, the speed of the plane is approximately 728.57 km/h, and the speed of the wind is approximately 48.57 km/h.
I hope this explanation helps you understand how to solve the problem. Good luck with your exam!