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A plane left 40 minutes late due to bad weather and in order to reach it's destination, 1600 km away in time,it had to increase it's speed by 400 km/h from it's usual speed. Find the usual speed of the plane :
- a)600 km/h
- b)750 km/h
- c)800 km/h
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A plane left 40 minutes late due to bad weather and in order to reach ...
Solution:-
Distance = 1600 km
Let the usual speed be = x km/h
now we know that
speed = distance /time
time = distance / speed
Usual time = 1600/x
Now due to bad weather the speed is increased be 400 km/ hr
which means new speed = 1600/x+400
Now it's given that the plain left 40 minutes late
which means new time = 1600/x+400 + 2/3 ( 40/60 = 2/3 hours)
1600/x = 1600/x+400 +2/3
1600/x-1600/x+400 = 2/3
1600(x+400)-1600x)/x(x+400) = 2/3
1600x + 640000-1600x/x²+400x = 2/3
640000 = 2/3(x²+400x)
640000 * 3/2 = x²+400x
960000 = x² +400x
0 = x²+400x-960000
0 = x² +1200x-800x-960000
0 = x( x+ 1200) - 800(x+1200)
0= (x+1200)(x-800)
x= -1200 or x= 800
Speed cannot be negative
∴ usual speed = 800 km/h
Distance = 1600 km
Let the usual speed be = x km/h
now we know that
speed = distance /time
time = distance / speed
Usual time = 1600/x
Now due to bad weather the speed is increased be 400 km/ hr
which means new speed = 1600/x+400
Now it's given that the plain left 40 minutes late
which means new time = 1600/x+400 + 2/3 ( 40/60 = 2/3 hours)
1600/x = 1600/x+400 +2/3
1600/x-1600/x+400 = 2/3
1600(x+400)-1600x)/x(x+400) = 2/3
1600x + 640000-1600x/x²+400x = 2/3
640000 = 2/3(x²+400x)
640000 * 3/2 = x²+400x
960000 = x² +400x
0 = x²+400x-960000
0 = x² +1200x-800x-960000
0 = x( x+ 1200) - 800(x+1200)
0= (x+1200)(x-800)
x= -1200 or x= 800
Speed cannot be negative
∴ usual speed = 800 km/h
Community Answer
A plane left 40 minutes late due to bad weather and in order to reach ...
Problem Solving Strategy:
- Use the formula:
Distance = Speed x Time
- Calculate the time taken to cover 1600 km at usual speed and increased speed.
- Use the time difference to find the usual speed.
Solution:
Let the usual speed of the plane be 'S' km/h.
The distance to be covered is 1600 km.
The time taken to cover the distance at the usual speed is:
Time = Distance / Speed
Time = 1600 / S hours
Due to bad weather, the plane left 40 minutes late. So the time available to cover the distance is:
Time = (1600 / S) - (40 / 60) hours
Time = (1600 / S) - (2 / 3) hours
The plane needs to cover the distance in time, so the time taken at the increased speed is:
Time = 1600 / (S + 400) hours
The difference in time taken at usual speed and increased speed is 40 minutes or 2/3 hours.
(1600 / S) - (2 / 3) - (1600 / (S + 400)) = (2 / 3)
Multiplying both sides by S(S+400) we get:
1600(S+400) - 2S(S+400)/3 -1600S = 2S(S+400)/3
Simplifying the above equation, we get:
S = 800 km/h
Therefore, the usual speed of the plane is 800 km/h. Hence, option (c) is the correct answer.
- Use the formula:
Distance = Speed x Time
- Calculate the time taken to cover 1600 km at usual speed and increased speed.
- Use the time difference to find the usual speed.
Solution:
Let the usual speed of the plane be 'S' km/h.
The distance to be covered is 1600 km.
The time taken to cover the distance at the usual speed is:
Time = Distance / Speed
Time = 1600 / S hours
Due to bad weather, the plane left 40 minutes late. So the time available to cover the distance is:
Time = (1600 / S) - (40 / 60) hours
Time = (1600 / S) - (2 / 3) hours
The plane needs to cover the distance in time, so the time taken at the increased speed is:
Time = 1600 / (S + 400) hours
The difference in time taken at usual speed and increased speed is 40 minutes or 2/3 hours.
(1600 / S) - (2 / 3) - (1600 / (S + 400)) = (2 / 3)
Multiplying both sides by S(S+400) we get:
1600(S+400) - 2S(S+400)/3 -1600S = 2S(S+400)/3
Simplifying the above equation, we get:
S = 800 km/h
Therefore, the usual speed of the plane is 800 km/h. Hence, option (c) is the correct answer.
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A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time,it had to increase its speed by 400 km/h from its usual speed. Find the usual speed of the plane :a)600 km/hb)750 km/hc)800 km/hd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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