A problem on distance

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Darya

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Jan 17, 2020
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A worker is deciding whether to go on his trip by train or plane. The plane has an average speed of 800km/h and flies to the destination for 2 h. An average speed of the train is 300km/h, 0,5 h needed to get to the destination.
The task is to find the minimum distance from which the trip by plane is shorter or equal to the trip by train.

I don't quite understand what the task is about. I thought it could be 1,5 hours going by plane which is 1,5*800=1200 but the correct answer is 720. Any hints? Thanks!
 
Incorrect translation? I don't think the times given are "to destination". Makes more sense if they are to the airport and to the train station. If this is the case, you need to write expressions for total time is travel and then solve the resulting inequality.
 
Darya said:
A worker is deciding whether to go on his trip by train or plane. The plane has an average speed of 800km/h and flies to the destination for 2 h. An average speed of the train is 300km/h, 0,5 h needed to get to the destination.
The task is to find the minimum distance from which the trip by plane is shorter or equal to the trip by train.

I don't quite understand what the task is about. I thought it could be 1,5 hours going by plane which is 1,5*800=1200 but the correct answer is 720. Any hints? Thanks!
Click to expand...
Why would you think "it could be 1.5 hours going by plane" when the problem says 2 h.? If the "plane has an average speed of 800 km/h ad flies to the destination for 2 h" then the destination is 1600 km away. The train, for 0.5 h at 300 km/h, will go 150 km, not 1600 so cannot reach he same destination. Please re-read the problem. As Lev888 suggested, perhaps the "2 h" and "1/2 h" are the times it takes to get to the airport and train station where you begin the trip, not to the destination.

If that is the case, let "d" be the distance, in km, of the trip itself. At 800 km/h, the trip will take d/800 hours. If it also take 2 hours to get to the airport, the total time is d/800+ 2. At 300 km/h, the trip, by train, will take d/300 hours. If it take 0.5 h to get to the train station, the total trip will take d/300+ 0.5 hours.

Solve d/800+ 2= d/300+ 0.5.
 
HallsofIvy said:
Why would you think "it could be 1.5 hours going by plane" when the problem says 2 h.? If the "plane has an average speed of 800 km/h ad flies to the destination for 2 h" then the destination is 1600 km away. The train, for 0.5 h at 300 km/h, will go 150 km, not 1600 so cannot reach he same destination. Please re-read the problem. As Lev888 suggested, perhaps the "2 h" and "1/2 h" are the times it takes to get to the airport and train station where you begin the trip, not to the destination.

If that is the case, let "d" be the distance, in km, of the trip itself. At 800 km/h, the trip will take d/800 hours. If it also take 2 hours to get to the airport, the total time is d/800+ 2. At 300 km/h, the trip, by train, will take d/300 hours. If it take 0.5 h to get to the train station, the total trip will take d/300+ 0.5 hours.

Solve d/800+ 2= d/300+ 0.5.
Click to expand...
Ommg, yeah, I must've made a mistake in translation AND comprehension of the problem. From your equation, I got the correct answer. Thanks a lot!!!
 
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