Hello! I'm on the brink of figuring out how to solve this problem but I just need a little help!
Question: A jet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangko to Tokyo.
A similar question to this and its answer is:
Lake Tahoe is a resort area east of San Francisco with an international airport nearby. A jet flew 4200 km from Lake Tahoe to Honolulu, Hawaii. On the return trip, the speed was increased by 100 km/h. If the total round trip took 13 hours, what was the jet's speed from lake Tahoe to Honolulu.
Solution:
Let x represent the speed, in km/h, during the first trip, from Lake Tahoe to Honolulu. The speed was increased by 100 km/h on the return trip, therefore x + 100 represents the speed from Honolulu to Lake Tahoe. As mentioned earlier, distance (d) is the product of speed (s) by time (t). Since d=st, then t=d/s. Use the following table to organize the given information and determine an equation.
| Distance (km) d | Speed (km/h) s | Time (hours) t=d/s
Lake Tahoe to Honolulu | 4200 | x | 4200/x
Honolulu to Lake Tahoe | 4200 | x + 100 | 4200/(x+100)
Total | 13
The round trip took 13 hours, so the sum of entries in the third column is 13.
4200/x + 4200/(x+100) = 13 Simplify this equation and solve for x.
To simplify, multiply each term by the product of the denominators, x(x+100).
4200 x(x+100) + 4200 x(x+100) = 13x(x+100)
x (x+100)
Reduce.
4200(x+100) + 4200x = 13x(x+100) Expand and simplify to standard form.
4200x + 420000 + 4200x = 13x(squared) +1300x Collect like terms and simplify
13x(squared) - 7100x - 420000 = 0 Factor to find the roots.
(13x + 700)(x - 600) = 0
x = -700/13 or x = 600
A negative value for x, which represents speed, does not make sense in this case. Therefore, the jet's speed from Lake Tahoe to Honolulu is 600km/h
NOW!
To apply this to the original question:
A jet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangko to Tokyo.
Since we are trying to find the speed I'm assuming that the equation is going to change to be s=d/t.
So to find the return speed I am thinking that the equation would look like s-200 = 4800/t - 2
Now this is where I start to get stuck. In order to mirror the similar equation I'm going to need an equation for the distance there. so s = 4800 / t.
In the similar equation we know time and distance but with this equation we only know the total distance. Not time or speed.
A graph might look like:
| Distance (km) d | Speed (km/h) s | Time (hours) |
Tokyo to Bangkok | 4800 | x | t |
Bangkok to Tokyo | 4800 | x - 200 | t - 2 |
Total | 9600 | | |
I think it would be good if I could get t - 2 to just equal t.
So perhaps.
t - 2 = 4800 / x-200
t = 2(4800/ x - 200)
t = 9600 / 2x - 400
t(2x -400) = 9600
...?
I don't know what I'm doing. I'm making a mess.
PLEASE HELP.
Question: A jet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangko to Tokyo.
A similar question to this and its answer is:
Lake Tahoe is a resort area east of San Francisco with an international airport nearby. A jet flew 4200 km from Lake Tahoe to Honolulu, Hawaii. On the return trip, the speed was increased by 100 km/h. If the total round trip took 13 hours, what was the jet's speed from lake Tahoe to Honolulu.
Solution:
Let x represent the speed, in km/h, during the first trip, from Lake Tahoe to Honolulu. The speed was increased by 100 km/h on the return trip, therefore x + 100 represents the speed from Honolulu to Lake Tahoe. As mentioned earlier, distance (d) is the product of speed (s) by time (t). Since d=st, then t=d/s. Use the following table to organize the given information and determine an equation.
| Distance (km) d | Speed (km/h) s | Time (hours) t=d/s
Lake Tahoe to Honolulu | 4200 | x | 4200/x
Honolulu to Lake Tahoe | 4200 | x + 100 | 4200/(x+100)
Total | 13
The round trip took 13 hours, so the sum of entries in the third column is 13.
4200/x + 4200/(x+100) = 13 Simplify this equation and solve for x.
To simplify, multiply each term by the product of the denominators, x(x+100).
4200 x(x+100) + 4200 x(x+100) = 13x(x+100)
x (x+100)
Reduce.
4200(x+100) + 4200x = 13x(x+100) Expand and simplify to standard form.
4200x + 420000 + 4200x = 13x(squared) +1300x Collect like terms and simplify
13x(squared) - 7100x - 420000 = 0 Factor to find the roots.
(13x + 700)(x - 600) = 0
x = -700/13 or x = 600
A negative value for x, which represents speed, does not make sense in this case. Therefore, the jet's speed from Lake Tahoe to Honolulu is 600km/h
NOW!
To apply this to the original question:
A jet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangko to Tokyo.
Since we are trying to find the speed I'm assuming that the equation is going to change to be s=d/t.
So to find the return speed I am thinking that the equation would look like s-200 = 4800/t - 2
Now this is where I start to get stuck. In order to mirror the similar equation I'm going to need an equation for the distance there. so s = 4800 / t.
In the similar equation we know time and distance but with this equation we only know the total distance. Not time or speed.
A graph might look like:
| Distance (km) d | Speed (km/h) s | Time (hours) |
Tokyo to Bangkok | 4800 | x | t |
Bangkok to Tokyo | 4800 | x - 200 | t - 2 |
Total | 9600 | | |
I think it would be good if I could get t - 2 to just equal t.
So perhaps.
t - 2 = 4800 / x-200
t = 2(4800/ x - 200)
t = 9600 / 2x - 400
t(2x -400) = 9600
...?
I don't know what I'm doing. I'm making a mess.
PLEASE HELP.